When you use the amount of infantry you would need to match up the other units in crop consumption, infantry are much better in every way except range and speed and they have the second highest speed. Around December I modified my Cavalry/Archer army to Infantry/Archer. Infantry get bonuses and still move quickly enough to get to the other side. Look at this comparison of 100 crop usage by each unit:
100 Infantry
atk-7,500 def-7,500 life-15,000 overload- 8,000 Spd-150-412
25 Cavalry
atk-4,375 def-4,375 life-12,500 overload- 2,500 Spd-300-825
50 Archer
atk-3,000 def-1,250 life-6,250 overload-2,000 Spd-125-343
10 Catapults (lol)
atk-3,000 def-1,000 life-4,500 overload-400 Spd-50-137
This is the base. WIth no stat or tech additions. With the tech additions, the difference is shown even more. (aside from the speed that's already shown)
With the field range of 1,260 (cat's with highest range on field), it takes infantry only 3 turns to reach the other side with a 24 remainder. Their range is 25.
When the opponent has turrets, i've noticed I lose less than than I do when using cavalry even though cavalry get there quicker. I mean less prestige loss, not less numbers lost. By this I mean that I might lose 2,000 cavalry, but only 6,000 infantry. 2,000 cavalry is 8,000 prestige while 6,000 infantry is only 6,000 prestige. If you use only catapults to kill level 10 turrets, the results are MUCH worse too. I generally have archers shooting at the turrets behind the infantry btw, so these numbers are taken from archers taking out a row with each attacking turn. Nothing can reach lv 10 turrets on the first turn forward. I have max attribute speed, max marching tech, max horse, and max manual. I've tested with all units.