I don't think there can be any question the Germans and Celts/Gauls were generally larger than Italians: that was the literary sterotype and the literature being written by and for (upper class) soldiers it could not have been completely made-up, and that these northern barbarians were generally large seems to be accepted by modern authorities (Todd 35).* The Roman literary cliche went something like this:
"The nation, which is now approaching, in a disorderly march, is one to whom nature has given minds and bodies of greater size than strength: for which reason, they bring to every contest more of terror, than of real vigour. The disaster of Rome may serve as a proof of this; they took the city, when every avenue lay open; but still a small band in the citadel and capitol are able to withstand them. Already tired of the slow proceedings of the siege, they retire and spread themselves over the face of the country. When gorged by food, and greedy draughts of wine, as soon as night comes on, they stretch themselves promiscuously, like brutes, near streams of water, without entrenchment, and without either guards or advanced posts; using at present, in consequence of success, still less caution than usual." (Livy 5.44)
This was part of a speech allegedly (it's a literary construction) given by Camillus to the people of Ardea whom he was trying to motivate to fight the Gauls who had taken over most of Rome in the aftermath of the disastrous Battle of the Allia in 390 BC. There are many similar references in Roman writers (especially in Livy), but this one contains all the usual cliches: the Gauls/Celts/Germans/etc are very large, brave and strong, and are formidable fighters, but their courage is not of the enduring sort. They lack discipline, endurance and training. That is to say, of the two core Roman military virtues they possessed virtus but not disciplina, and it was the latter that was considered peculiar to the Romans (Mattern 203, Phang 38). Their virtus and their physical size and strength made them very formidable, especially in the early stages of battle, but made them unsuited to extended fighting where wounds and exhaustion would cause their animus to fail them, a direct result of their lack of disciplina. Livy's account of Hannibal's march through the Italian swamps after the Battle of the Trebia in 217 BC emphasises this lack of physical endurance:
"...for [the Gauls], it had been found, want firmness to support fatigue. The troops in the van, though almost swallowed in mud, and frequently plunging entirely under water, yet followed the standards wherever their guides led the way, but the Gauls could neither keep their feet, nor, when they fell, raise themselves out of the gulfs, which were formed by the river from the steepness of its banks. They were destitute of spirits and almost hope; and while some, with difficulty, dragged on their enfeebled limbs, others, exhausted by the length of way, having once fallen, lay there, and died among the cattle, of which great numbers also perished. But what utterly overpowered them, was the want of sleep, which they had now endured for four days and three nights..." (Livy 22.2).
Here the Gauls are specifically contrasted with professional soldiers, the mercenaries that made up the majority of Carthaginian armies. 'Real' soldiers, as the Romans (quite rightly) considered themselves, were trained and had physical and moral endurance, which the Gauls lacked, despite their physical abilities and courage in battle.
However, the Romans of course did not cede superior virtus entirely to the Gauls: note that of the two major accounts we have of duels between individual Romans and Gauls (Titus Manlius Torquatus and Marcus Valerius Corvus), the Romans win. The Romans must have been very proud of these stories, though they were not necessarily typical: we might not expect Livy, a staunch patriot, to recount every instance in which such a fight did not go in the favour of Romans. There is clearly some tension on the part of Livy at least regarding physical appearance: regarding the duel of Titus Manlius c. 361 BC, Livy specifically mentions that while the Gaul was enormous the Roman was of "a middling stature for a soldier" (7.10). Livy also makes several mentions in later books of particular acts of bravery by Roman centurions, and he especially emphasises the remarkable physical size of these men (25.19, 26.5). Size was clearly viewed as an impressive military quality, for obvious reasons. That the Gauls appear to have had size in abundance was therefore a legitimate reason for them to be respected as warriors, but an even better reason for the Romans to take special pride in their humiliation and defeat.
I would say then that the Germans and Celts/Gauls were very much, on average "bigger" than the Romans, but they were not necessarily "better at fighting". As the Romans considered the essential military virtues to be not only manly courage or virtus but also the physical and moral quality of disciplina, a product of training and hard work, that the Germans and Gauls/Celts did not possess the latter was really a damning indictment of their military ability. They were good fighters, and the Romans respected them as such, but the Romans did not view them as having the qualities of soldiers. Rome's consistent success on the battlefield against Germans and Celts/Gauls after the 3rd century BC (with the prominent exception of Arausio) to some extent must validate the Roman view that organisation, order, training and discipline are at least as important as physical ability and courage in winning battles. Of course, while the Romans (especially Caesar, who mentions Gallic virtus a lot: see Rawlings 179) were often impressed by barbarian courage, that is also not to say they viewed them as more courageous than themselves: merely that they were worthy enemies, making it all the more impressive a victory for the Romans.
The question of whether the Germans and Gauls/Celts were better fighters than the Romans aside (wealthy Gauls/Celts who were similarly equipped to legionaries would have been particularly formidable fighters), there is however no question that the Romans possessed "superior military organisation". They had superior manpower, superior training, superior logistics and superior tactics. The Romans had the capacity to recruit, train, organise and deploy effectively innumerable numbers of well-equipped, good-quality soldiers for extended periods such that they had no close military competitors after the Second Punic War. That the Romans lost battles against 'barbarians' at all is a testament to the impressive military power of less well-organised but formidable peoples such as the Senones, Teutones or Cimbri. But these reverses made the Roman military organisation no less superior, only fallible.
*The literature may not seem like proof to some people, but that many military writers who actually lived at the time and encountered these peoples consistently wrote that they were generally quite large I think is fair evidence that this was a reality. The burden of proof in my view is really on those who don't believe the accounts of those who were actually there to provide conflicting evidence. There is however some good follow-up on this matter in the discussion below from /u/Aerandir, /u/XenophonTheAthenian. /u/Steko has linked an interesting PhD paper on the matter. Annoyingly, this issue does not appear to be specifically addressed in the books I have consulted on the topic.
Sources:
Mattern, Susan P., Rome and the Enemy: Imperial Strategy in the Principate, University of California Press, Los Angeles, 1999.
Phang, Sara E. Roman Military Service: Ideologies of Discipline in the Late Republic and Early Principate, New York, Cambridge University Press, 2008.
Rawlings, Louis. Caesar’s Portrayal of Gauls as Warriors, from Julius Caesar as Artful Reporter: The War Commentaries as Political Instruments eds. Kathryn Welch and Anton Powell, London: Duckworth/The Classical Press of Wales, 1998, 171-192.
Todd, Malcolm. The Early Germans: Second Edition. Oxford: Blackwell Publishing, 2004.
There was definitely a difference in length between the ancients and their barbarian neighbors; the archaeological evidence is pretty conclusive. I will be using Swedish data, which will here be considered a representative for the Germanic peoples. The problem is that we have fewer excavated burials for this era than for the Christian middle ages, which makes it hard to create robust theories. The later stone churches of the middle ages locked the villages to the land, stopping migrations and creating large graveyards in use for centuries.
But there is a wealth of medieval cemeteries which has yielded great evidence for an accurate analysis. The average body height for men varied somewhere just above 170 cm. The interesting part is the regional differences, because they archaeologically prove the correlation between how many animal proteins is consumed by a man and his body height.
The north-eastern mountainous provinces of Dalecarlia and Jämtland were then heavily reliant on livestock keeping, and had an average height of 173 cm. The fertile, grain producing soils of Scania, at the southernmost tip of Sweden, had a lower average though. There, it was just under 170 cm.
The biggest difference between the Romans and the barbarians is that the Romans' dominating agricultural produce was corn (mostly wheat). Cereals are definitely the way to utilize the available arable land to the fullest extent. But the Germanic peoples had plenty of land to practice slash-and-burn agriculture on, giving them lots of grazing land for cattle.
Sources: Janken Myrdal, The Agrarian history of Sweden
Follow up queston here,
from what I've understood the Romans lived in perpetual fear that the Celtic clans that were spread all over Europe might stop with their infighting and come on over to pillage the young empire into the ground. As far as I can recall Rome was beset by Barbarians multiple times in early history which then had to be paid off to leave it in one piece.
If all of the above is right (if it isn't please correct me), didn't the Celtic tribis inspire the Romans towards superior military organization in the first place so as to withstand the raving hordes?