Lately I've done well against jax with Nasus and surprisingly Brand.
As Nasus I start with ninja tabi early or dorans shield + boots, focus on farming Q (siphoning strike), zone him with E (spirit fire) (great when dueling also as it reduces armor) build randuins or frozen heart. For damage build trinity, gunblade or sanguines. I like to build Spirit visage for additional CDR, MR, life steal/HP regen and hp. I run from him when he dodges and stuns. If I engage I make sure he is constantly slowed by W, while my E decreases his armor. I run armor pen runes, hp per lvl seals, MR glyphs, x2 Move speed quints and x1 Life steal quint. Late game I am at roughly 40% life steal and Q hits like a truck with sheen process.
As brand I run x2MS quints again, 1 CDR per lvl quint, CDR per lvl glyphs, HP per lvl seals. For masteries I also focus on CDR. The key is to keep him at a distance (obviously). I like to take prospector's ring to start and boots, rush rylais right after, from here it's situational. Blast him with pillar of flame when he tries to farm or push minions, hit conflagation and stun when he tries to get near me. Rinse, repeat, you should be able to push the minions much better than him, just keep your distance and be mindful of ganks.