SotD is decent on AS champs, and the ArmPen on the active is nice on tanky dps. Also the sword is effective against a few other champs, not just Jax. If you get blinded by teemo, SotD's active lets you still hit while blinded, oddly but works. And Sivir's passive gives her a good amount of dodge. And Udyr's passive.
Personally tho, everyone hates having to sacrifice an item just to build against a specific champion. Hextech Sweeper, Lightbringer, Sword of the Divine, Executioner's Calling.
When you play, try to make a good team comp that can handle most champs. Jax doesnt do as well against AP nukes and CC, he's just an anti-AA carry. If your team is full of AA'ers well, im sorry but you guys got yourselves ****ed. Next time you see a Jax, have your Mage focus him.