Just so everyone knows, comments are being removed because no one has given a clear, sourced answer that considers both the allure of Britain and the repulsiveness of Germania to the Romans.

Since no-one has answered this I think I can provide some information on this, and will throw my hat into this graveyard despite me being all but ignorant on Roman Britain. Which is why I will mainly focus on the assumption that underlies your question, that the Romans put so much into invading Britain compared to conquering Germany. I must preface this with the caveat lector that this is a debated topic, and just my personal interpretation of the discussion. But with this out of the way, let's get right down to your question. Did they? You seem to be assuming that the Romans did not invest many resources in pacifying and conquering Germania, but they absolutely did. If not, I apologize for my assumption.

After Caesar had established the Rhine both as a political as well as an ethnographic border - Gauls to the left, Germans to the right, which is a neat division but not very reflective of reality - the Roman empire was involved in heavy campaigning and infrastructural measures for decades in Germany right of the Rhine. Augustus had ordered the legions stationed directly at the Rhine, probably as a reaction to the continuing threat that German groups posed to the security of Gaul, evidenced in the defeat of Lollius, gouvernor of Gallia, against Sugambrians, Tencteres and Usipetes in 16 BC, during which the eagle of the 5th legion was lost.

Several legions with auxiliary units where involved in pacifying the alpine tribes as well as the northern Alpine foothills in southern Germany under Drusus and Tiberius in 15 BC, which laid the groundwork for establishing the province of Raetia in southern Germany. This campaign involved heavy fighting to bring the alpine passes under control, which is evidenced by leaden sling balls and heavy artillery bolt tips that have been found at the Döttenbichl hill in southern Germany and around the Septimer pass in Switzerland.

The following years saw increased military activity across the Rhine, from 12 to 8 BC Drusus led several campaigns in Northern Germany that saw the Roman operating radius extended towards the river Elbe. After his death his brother Tiberius completed the operations, which saw northern Germany largely pacified and under Roman control, with one of the major antagonists to Roman power, the Sugambrians, out of the picture. But in the year 1, a first great challenge to Roman rule, the 'immense war' (so called by the historian Velleius Paterculus, who served as prefecti in that war) broke out, at first fought with some success by the gouvernor Vinicius, but subsequently requiring the involvement of Tiberius and a sizeable army. But this revolt, too, was brought down with success, with Velleius Paterculus stating that

Nothing remained to be conquered in Germany except the people of the Marcomanni [II, 108]

The Marcomanni under their king Marbod had withdrawn to the Hercynian forest, the modern Bohemian basin. To remove this last obstacle to Roman power, Tiberius organized a large two-pronged operation, himself leading six or seven legions out of the camp at Carnuntum (on the Danube just to the east of modern Vienna), while another two or three legions were to join him from the Rhine. That's up to ten legions, together with thier auxiliaries and cavalry. Over a third of the whole Roman army! That is quite an investment if you ask me, and it probably would have been enough. But a problem arose when the newly conquered Pannonians rose up in revolt, a revolt that involved Illyria and quickly threatened Macedonia and Italy itself - Tiberius had to return, and made peace with Marbod to deal with the Pannonian revolt first. The second desaster followed three years later and is well known. In a catastrophically effective ambush, the provincial legate P. Quinctilius Varus was killed and his 17th, 18th and 19th legion wiped out, probably near Kalkriese in northern Germany, the battle of the Teutoburg Forest.

With this battle, Rome not only lost three important legions, at a time when it could little afford such losses, but consequently also lost control of its territories across the Rhine. The shock of this defeat can not be underestimated. The Romans were afraid of the Germans as it was, but this only made things worse. Ever since the invasion from the Germanic tribes of the Cimbrians and Teutones, who had defeated the Romans at Noreia and Arausio, only to be all but wiped out by Marius (but for a time, a veritable threat to Rome itself seemed to be imminent), fear of the furor teutonicus, of the warlike and brutal barbarians to the north, was a common trope in Roman politics and literature. Caesar used it as justification for his campaigns in Gaul, stating the danger of Germanic occupation of Gaul next to a Roman province [bell. Gall. 1, 28, 5], or the danger of cooperation with the Gauls, this probably was also a motivating factor for Caesar crossing the Rhine, to demonstrate Roman military power and intimidate the Germans. When Lollius lost his battle and the eagle of the 5th legion in 16 BC, this has to be seen in this psychological light, especially considering that a big part of Augustean propaganda had been the repatriation of the legionary eagles Crassus had lost against the Parthians.

This desire for security from the Germans probably was one of the big motivating factors in subjugating the lands between the Rhine and the Elbe, and until this point, they had been successful. Roman camps were spread throughout Germany, and not only that - towns after the Roman pattern were already built throughout the newly won province! Evidence for this can be found in an often disregarded passage of Cassius Dio:

The Romans were holding portions of [Germany] — not entire regions, but merely such districts as happened to have been subdued, so that no record has been made of the fact — and soldiers of theirs were wintering there and cities were being founded. The barbarians were adapting themselves to Roman ways, were becoming accustomed to hold markets, and were meeting in peaceful assemblages. [LVI,18,1-2]

But we have not only this literary evidence, which is of course a bit thin - for around 20 years, we know of one such city. At Lahnau-Waldgirmes, which lies near modern Gießen, a roman trading station with a large forum, was discovered. It was abandoned probably shortly after 9 AD, but it shows that the Romans were already well on their way in establishing the usual infrastructure of Roman civilization, roads, towns with forum after the Roman pattern where people could congregate and trade. To finally get around to Britain, this echoes a famous and oft-cited passage in Tacitus Agricola, his account of the gouvernorship of Britain by his father-in-law, Agricola, which is examplary of the way the Romans integrated new territories into their empire and deserves being quoted in full:

The following winter passed without disturbance, and was employed in salutary measures. For, to accustom to rest and repose through the charms of luxury a population scattered and barbarous and therefore inclined to war, Agricola gave private encouragement and public aid to the building of temples, courts of justice and dwelling-houses, praising the energetic, and reproving the indolent. Thus an honourable rivalry took the place of compulsion. He likewise provided a liberal education for the sons of the chiefs, and showed such a preference for the natural powers of the Britons over the industry of the Gauls that they who lately disdained the tongue of Rome now coveted its eloquence. Hence, too, a liking sprang up for our style of dress, and the toga became fashionable. Step by step they were led to things which dispose to vice, the lounge, the bath, the elegant banquet. All this in their ignorance, they called civilization, when it was but a part of their servitude.

Germany was largely pacified. Towns were built after the Roman fashion, taxes were levied, Varus judged cases as a Roman gouvernor was used to do. Agricola in Britain was much more succesful in this than Varus was in Germany, obviously. But it was not for a lack of trying. The defeat of Varus came at a very unfortunate point in time. The campaigns in Germany and the Pannonian revolt had already drained Roman resources. Augustus had to hastily raise emergency levies to stabilize the Rhine frontier. And while under Tiberius, Germanicus was to succesfully campaign in Germany again, Tiberius recalled him and put an end to these operations in 16 AD. One reason for this was that the support base in Gaul and Germany left of the Rhine was probably exhausted for the time being and operations became difficult to sustain. Another reason is probably that Tiberius was aware that the far-ranging campaigns of Germanicus always brought the risk of another Varian catastrophe with them, which would be a very hard loss to absorb, both on the military and the political level - and on the political level, the Tiberian policy of withdrawing to the Rhine and using diplomacy to break up the Germanic power-blocs and play the rulers against each other was much more successful anyway and brought security to the Rhine frontier. And even then expansion didn't fully stop. Roman control of the lands along the lower Main river and the Neckar was gradually extended during the late 1st and early 2nd centuries, and again with massive investments. The Roman forum of Lopodunum (near modern Heidelberg) is one of the largest of its kind north of the alps!

Because I love the droning sound of my own voice, here's a post that addresses why the Romans never bothered to conquer Germany.

As for Britannia? That is more about about politics than anything else. Claudius had been acclaimed emperor by the soldiers following the murder of Gaius (i.e. Caligula) in 41 CE. He definitely was not the first choice - the senate was busy arguing over which of them would become the Princeps. He was a bookish type, fond of history and had been been left alive under Gaius because he represented no political threat.

So Claudius begins his rule without a real strong political base, his physical characteristics were not always the most impressive, he did not have the traditional career of the cursus honorum which meant he lacked governing and command experience (although he got an ornamental consulship). In short he's massively overdrawn at the bank of auctoritas and dignitas (branches in every major urbs). He's got his family's impressive history in his favour but that's really about it - and he knows this.

So what he needs is a strong military victory to burnish his very faint credentials - he needs to really win the title of imperator that will raise his standings and make his rule more secure. Britannia is distant, mysterious, yet close to Gaul. Caesar went there and won some battles but couldn't capture it - how impressive would it be if he could accomplish what even the great Caesar could not?

So the campaign, while still significant, was not as demanding as say a German campaign would have been. It involved 4 legions and an equivalent number of auxilia - probably 40,000ish soldiers in all. Rome certainly put more resources in things like the conquest of Dacia.

What I'm hoping one of the mods or flaired users might add is why they kept the province since it was relatively poor and might not have benefited the treasury at all? Hadrian had quit Mesopotamia (conquered by Trajan) as undefendable. My gut suspicion is that Nero wasn't terribly focused on the administration of the empire and by the time you got Vespasian, it'd been in the empire for almost a generation and he didn't want to start off his rule (following a bloody civil war) with shrinking the empire.