AP gives 1:1 on Leap Strike and Ult, and .8:1 on Stun.
Jax's standard sequence is:
Whack them 3 times and get Ult
Run like hell
For 1v1 damage, each point of Attack damage adds 3 damage to this sequence. Each point of AP adds 2.8 damage to this sequence.
The big difference is that AP gives AoE damage on Counterstrike, and that AP is about half as expensive as attack damage.
If you do go AP, the best items are the "Hybrid" items (Nashor's Tooth, Guinsoo's Rageblade, Sheen/Lichbane/Trinity Force). Rylai's is also decent to proc slows on Leap/Counterstrike hits, but Frozen Mallet gives a stronger and longer slow and can be triggered just as easily.