Jax is OP Because his Old Ultimate is now his passive.
And he Gets the Dodge and a stun in 1 move.
Then comes empower, It can Increase the damage of ANY of his moves.
But His Ultimate is useless unless you're going Hybrid.
Jax is definitely not OP.
Let's put in the counterarguments to your "reasoning."
Old Ulti=Passive: Why would this be imba? Most of the time early game, he won't even proc this passive effectively much. He's too busy waiting for last hits to focus on attack speed.
Dodge and Stun: May I introduce you to a single target cc? You can cc him to make him waste his counterstrike. Malphite excels at this, and he's not the only one. Also, Jax CANNOT DODGE NON-ON-HIT SPELLS! So if Soraka trolls and goes top, ALL OF HER STARCALL SHOTS IN YOUR RANGE WILL HIT YOU FOR FULL DAMAGE, NO MATTER WHAT.
Empower: ... Not sure if trolling or just retarded. Empower doesn't boost EVERYTHING, as you can see with Counter Strike. And Jax needs to get in range for this ability to be effective, and this can easily be shut down, unless he's in Leap Strike range.
New Ultimate: Well, can't argue with you there. You need a good balance of ad and ap to get both resistances.