If one is getting daphnia and other things and not pooping much, while the other gets pellets and drops logs, i would suspect it is also the diet to a certain amount that is causing the differing fecal consistencies. The pellets likely have a fibrous bran style vegetative base which helps bind them together, and an Axie, being a carnivorous critter, doesn't have the herbivorous stomach to digest the pellets substrate.
Fish farm pellets like the salmon pellets soem reccommend on here to feed to axies are made to be droped in the water with fish and to hold together until eaten, plain ground meat dissolves rapidly and dried hard like beef jerky, or goes mouldy fast if still moist. but fish pellets are usually soft while still high meat protein. this is done with mixes of bran style base substrate and glycerine and other water free moisteners.
I suspect the logs are undigested pellet base substrate and binder after having the food value digested off them on their way through the gut.