One thing that's very easy to forget is that autocracy was popular. In a sense, anyway. The proposal to give Augustus the dictatorship was a popular decision. (Velleius 2.89.5) Even Tacitus, who was among the fiercest critics of the imperial system, had to begrudgingly admit that the lives of ordinary people were improved by the establishment of a stable autocracy. (Annals 1.2.1) The Senate, however, was far less congenial to empire, which was unsurprising given that that meant the end of their power. Unfortunately, they still had to exist, as the emperors could not really survive without the Senate's experienced statesmen, yet they also became incapable of effectively stopping the emperors. At most they might attempt to place some restrictions – the Lex de Imperio Vespasiani may (or may not) have been the senate taking a stand and codifying the emperor's powers constitutionally – but were ultimately very much beholden to the emperors' will. Take, for example, Tiberius' maiestas trials (like that of Cremutius Cordus in Annals Book 4) or the infighting in the senate under Domitian (Tac. Agricola 44-45). This is the sort of environment in which our sources were operating – where the more literate, active contemporary writers generally had a senatorial agenda, whilst the pro-imperial masses left behind nothing.

When it comes to the 'decadent' emperors – Caligula, Nero and Domitian being the big ones of the 1st Century – a pretty consistent pattern emerges, which is that they were well-received by the people at large, but rather less so by the more aristocratic faction (apart from those who were already their stooges), and tended to do things with mass appeal. Caligula, for example, was a passionate supporter of the Green team in the chariot races (Suetonius Gaius Caligula 55), whilst Domitian had the number of laps decreased so that there would be more races per day (Suetonius Domitian 4). Nero, too, was an active sponsor of charioteering. (Dio 61.6) However, their treatment of the senate was somewhat less conciliatory. We all know of the Incitatus incident, where Caligula allegedly made his horse consul, (Suet. Calig. 55) but there were also Nero's maiestas trials (Tac. Ann. 14.48-49) and Domitian's abuses.

And it is unsurprising that we should see this pattern, for who were writing history but senators? Tacitus (c.56-120) was a senator, as was Cassius Dio (c.155-235). There are exceptions, of course. Suetonius (c.69-122), whilst an equestrian, was very much of senatorial leaning, whilst Velleius Paterculus (c.19 BC-AD 31) was a senator but very much a shill of the Augustan and Tiberian regimes (until just before the downfall of Sejanus in 31, leading some to speculate that he was a victim of the anti-Sejanus purge). A few of the emperors were denigrated from the start, others had excuses made for them. Caligula, for example, was actually popular among senators to begin with, (Suet. Calig. 13-14) and so it is entirely possible that the narrative that he suddenly went mad was a cover to absolve the senators of blame for having supported him earlier on. Domitian, on the other hand, acceded more or less purely though relation to his brother, Titus, and so we get Suetonius claiming that he had always been plotting his rise to power.

As to whether opinions are applicable beyond a single author, it's a bit complicated. The history of the early empire is (as in most cases) largely one written by the losers, an especially sore loser in the case of Tacitus. Plenty of senators did OK and didn't mind too much, with Velleius being the key example, but there were also men like Frontinus, the aqueducts commissioner under Nerva and Trajan, whose de Aquaeductu has very little to comment about any of the emperors at all. Still, you did find senators featuring prominently in opposition – the senator Thrasea Paetus, his father-in-law Caecina Paetus and his son-in-law Helvidius Priscus all opposed the emperors in some way, and were, thanks to their acts of opposition, executed by various emperors: Caecina Paetus by Claudius, Thrasea Paetus by Nero and Helvidius Priscus by Vespasian. In effect, the image we get of the 'bad' 1st Century emperors was produced by the most vocal part of a somewhat disempowered minority – still more powerful than your average Joeus Bloggus, but not quite as powerful as they would have liked to be.