I had the E12A for years as my primary amp. It has driven every headphone I own or have owned perfectly fine, including the HD598, Fidelity X2, 600ohm Superlux HD660, etc. The full list of gear is in my profile.
And as others have mentioned, the HD598 needs no amp and is powered just fine by your FiiO DAP. I owned the 598 for years.
I only added an A5 to the stable because I came across a great deal, and because I will eventually buy some planars and electrostats. Otherwise, I still use the E12A to this day.
As I mentioned previously, either E12A or A5 are more than enough for your HD598 (as is your FiiO DAP by itself). Be aware that adding an amp is just more bulk to haul around, more cables, more stuff to charge, etc. It gets old, believe me. And it can color the sound by being an extra processing step in the chain.
But, if you’re insistent on getting an amp, based on what gear you use I would get the E12A Mont Blanc for the significantly longer battery life. It is so close in sound to the A5, that in a blind test you will be unable to tell the difference.