In general it tries to avoid eating at all. One time I caught it putting it's hoof down its throat.
I think that "je wolno" gives the same emphasis as "eating slowly" - on the 'slowly' part.
They are similar. I would say that "powoli" is often used when you ask someone to slow down (also "wolniej" - slower) or when someone does something slowly and precisely/thoroughly. On the other hand, "wolno" is often used when something is being done too slowly. But generally, they are synonyms.
It is often connotation but you would need some context to determine if this is the case.