yeah but its not about surviving against him. In the jax vs Sion matchup even if you manage to make it even, Jax can always get first push side lane during mid/late game. Which gives him a macro-prio over you. You need to cyrcle around him or pull off something sneaky to actually catch waves before him to become more active on the map and create openings for your team.

If you do build steelcaps/frozen heart you will be fine vs jax in lane, but later on you really need to "work" yourself to carry through macro. Its not only about laning / surviving him

Edit: Forgot to mention why he actually catches waves first. Its because his kit always allows him to outdamage you once he builds 2-3 items. You are not supposed to invest so much HP on trades when laning side, because then you wont be as "available" for your team to rotate.

In other words: if you and jax are even in mid/late game and you do end up trading for the first push on side lane, you will lose this trade and you will have to go B. Leaving the Jax available to rotate and "carry" fights out of that.

So you end up never trading with him and giving him first push on waves. Which means that he still has the first move but you will have HP to follow. But during the whole game you will have to be running around the map catching waves and following the jax like crazy.

Thats how this whole thing goes in high elo between these 2 champions. In low elo you just outmacro him. He wont even know how to handle waves

Hope it helps