Hang on, the training of soldiers is more a function of whether or not they're professional soldiers than which era they're from. A roman imperial soldier would as you point out, train. But not in the sense that we train today, they would train marching, swordsmanship, formation fighting, spear throwing and so on, essentially the skills required to preform their duty in the field. Now, this would also make them stronger and given them better endurance but there is no mention in for example De Re Militari of specifically training to build muscle.

The greeks however were another matter entirely. The Phalanx armies were not, with the partial exception of Sparta, professional armies. They were citizen soldiers and as such would undertake zero training in peace time and have little or no time for training in war time. The greeks themselves had no illusions about the average fitness of their phalanxes. Xenophone writes:

Armies made up of citizens include men who are already old and others who have not yet come to their prime. Furthermore, in every city very few men train their bodies.

Another example is from Plato who wrote:

...When a lean, sinewy, sunburnt poor man is stationed in battle beside a rich man bred in the shade, and burdened with superfluous flesh, and sees him panting and helpless...

This is decidedly NOT a description of the godlike physiques seen in statues and busts, so where did all of that come from? Greek male beauty standards. I think you can safely assume that the ripped greek men immoralized in marble have about as much in common with the average greek man as the underwear models on billboards have with the average man today. In both cases the model is the absolute pinnacle of beauty further enhanced by the hand of an artist.

So here we have two roughly contemporary armies, one is a professional army that drills the men, the other is an army of citizen soldiers that does not. I think we can safely assume that the average imperial roman legionnaire would have been significantly fitter than the average greek phalanx because the roman legionnaire is a professional soldier.

And then the roman empire fell and with it the professional armies of western Europe. A rather dark period sometimes called the dark ages for no apparent reason followed in western europe. This era was characterized by small numbers of professional soldiers, generally speaking knights, and large numbers of leavies who were again, not professional soldiers. A knight would train in the sense that he would hunt, ride, practice with his weapons and so on, not unlike a professional soldier in a roman army but he would not generally work out for the sake of fitness alone. Eventually semi-professional infantry forces arise, swiss pike for example. Men who train at least regularly although they were generally not professional soldiers.

As nation states strengthen and centralize their power they start again maintaining professional armies and again we see the rise of drills. In fact, drills so similar to those of roman legionnaires they were initially called roman drills. The focus is still on marching and fighting, not physical fitness in itself. The rise of muskets introduces new elements to the drill, the firing, reloading and general care asociated with black powder weaponry but in a very general sense it is still a roman drill. March, fight, obey. In some cases this is take to extremes but again, the purpose is not fitness in itself but combat effectiveness.

This continues basically up to the modern day. The focus of the training is not on fitness itself but on combat effectiveness of the soldiers. Only in the modern day has significant focus been places on improving the fitness of the soldiers. Why? Because for the first time in human history the majority of the population are no longer manual labourers. For the first time in history it is necessary to improve the fitness of new recruits beyond the specific conditioning required by their assigned role.

TL;DR - The amount of training recieved by a soldier depends on whether or not he is a full/part time soldier or a hastily drafted citizen, not which time period he is from.