The difference between Jungle Nunu and Jungle Eve is like night and day
With the changes in the jungle i just played some games as Eve, Jax, and Nunu.
Eve was a nightmare where i died and recalled a lot. while i tried to find some route she could handle. She only started really working well after 13 min of pain full jungleing and by that time laning phase is almost over. Eve is squishy and melee so Skirmisher + Devourer is not as usefull as with Jax.
Nunu on the other hand was easier than normal as he just hops around jungle butchering mobs and rarely losing health. In fact after ganking i went back into jungle to heal up some. I was using Poachers and Magnus mostly.
Jax is in the middle of these 2 extremes. Early on Jax takes some damage, but not as much as eve with his dodge and stun. I am better with Jax than Eve too and i know how to cancel and double hit with Jax. Skirmisher + Devourer is great on Jax.
? You should buy mana pots with him, if anything, not HP pots.