I've done a fair bit of testing of ePSXe 2.0, and provided you stick to the packed in plugins (or optionally, GPU BladeSoft), I can't fault it as heavily for the purposes of playing FFT as I used to. The default video plugin is slow, but lovely on capable machines. BladeSoft is also progressing nicely, and brilliant to use if (currently) you like native console display resolution, but better. The hacked Pete's plugin is much faster than the former two, but don't look at me if you have visual issues (I can still make it break in each Final Fantasy).
I haven't tested each and every ASM or patch known as working elsewhere, but ePSXe 2.0 has surprised me in general. It's still very much discouraged for testing ASM, but I won't fault anyone using it for just wanting to play the game or the mods offered here. I've done a lot of testing not just with FFT, but with 200~ other PlayStation games since its release, and I can only recommend Mednafen or PCSX-R over it on the grounds of utmost accuracy at the core; the visual result is currently superior on ePSXe, and I can't break it as easily as I used to. In the realm of ASM, Mednafen still reigns supreme, and PCSX-R still holds a higher seat, but I'm done dissing ePSXe as long as you're on 2.0 or above. It really did improve that much in the last release.
tl;dr - ePSXe is no longer a naughty word here as long as it's version 2.0 or greater.