I can answer your 'headline' question. The average Roman soldier, working from averages for modern, fit and active men of their physical size, needed 3000 calories a day, and they got this amount in their routine rations. Most of their calories came from their grain ration of 850 grams per day. This grain was mostly eaten as porridge and bread (Erdkamp 298). Indeed, the allocation of such specific amounts of grain was a key rationale for the standardisation of unit sizes in the Augustan period. The legionary ate slightly differently in different parts of the empire, but derived their remaining nutritional requirements from meat, cheese, vegetables, olive oil, sour wine and salt. They carried a daily ration of 1-1.3 kg of food, oil and wine (Roth 67).

The Roman contubernia (plural), or 'tent-mates', slept, prepared food (the bread they ate daily from their grain had to be made fresh every day) and ate together. There were no communal messes like a modern military. Greek hoplites, on the other hand, tended to individually purchase food, which Roman soldiers generally did not do. By historical standards the highly organised and routine system of Roman army food supply and consumption made the Roman soldier quite well fed (Roth 330). This food supply was a central element in the endurance of Roman armies in the field, and was essential to the morale and effectiveness of Roman soldiers: the Romans went to great lengths in the Imperial period to send mainstays such as olive oil, fish sauce, spices and wine to even the most obscure postings (Coulston 17-8; Roth 332). Roman soldiers considered olive oil to be particularly important: on campaign in Arabia under Aelius Gallus c. 25 BC , the men were "reduced" to eating butter with their bread instead of olive oil, which they considered a genuine hardship (Roth 35).

I am far from an expert on the Greeks, but their logistical system was nowhere near as advanced and organised as was that of the Romans in the Imperial period. Alexander the Great deserves a special mention for a particularly impressive effort in managing to feed his army during a lightning campaign in (mostly) hostile territory (Engels 121-2). However, this paled in comparison to the Roman ability to, through their control of Mediterranean and extremely developed strategic logistics, supply their soldiers with olive oil and wine for hundreds of years, no matter how obscure their outpost in Britain, Arabia or Mesopotamia.

Sources:

Coulston, Jon. "Courage and Cowardice in the Roman Imperial Army." War in History, Vol. 20, No. 1, 2013, 7-31.

Engels, Donald W.. Alexander the Great and the Logistics of the Macedonian Army. Los Angeles, University of California Press, 1978.

Erdkamp, Paul. Hunger and the Sword; Warfare and Food Supply in Roman Republican Wars (264 - 30 B.C.), Amsterdam, J. C. Gieben, 1998.

Roth, Jonathon P. The Logistics of the Roman Army at War (264 BC- AD 235), Boston: Brill, 1999.