AD Fizz vs Jax

Me playing AD Fizz for the first time, gave me a Jax vibe. For some reason though, I felt like he was actually way better than Jax, at like, everything. I build him Skirmisher's w/ Devourer, Botrk, Triforce, Hextech, and Bezerker Greaves. If the game lasted long enough I probably would have gone Liandris for more HP shred or a Frozen Mallet. They have, overall pretty similar builds, but I feel like Fizz pulls it off better. His Q is very similar with Jax's only Fizz's applies on hit effects. Fizz has HP shred + passive bonus magic damage on attacks with his W, while Jax has his empowered attack. Fizz has potential to dodge all abilities instead of just autoattacks while Jax can only dodge autoattacks, however he can attack during counterstrike. Fizz's ult with the damage amplifiers etc overall I just feel like is better than Jax's resistances + bonus damage on third AA. Is there really a reason to play Jax over Fizz, with Hextech and Botrk you pretty much have Jax lvl sustain with super HP shred. I'm talking 1v1ing a decently fed Darius with ease.

Edit: I don't know if I should really call it AD Fizz more of an on-hit Fizz.