I´d say Jax has a easier time in general, thanks to his E blocking autos and reducing AOE damage along with his ulti for resistances.
It lets him participate in teamfights and be relevant, that added with the fact that he has some of the best scalings and stacking stuff in the game he does well all around.
Tryndamere has a terrible time if he gets CCed and takes a lot of damage right from the start, with his ulti blown he can only run away, to compare with jax who could soak a number of hits without being forced out.
As for 1v1.......honestly in lane jax probably wins for a while as long as he plays his cards right, trynd doesnt have any way to get around the E easily.
Post 6 its a closer call, but it shouldnt be impossible for a high damage build jax to force trynd to ulti quickly and then protect himself with E.
Of course such a build is probably less effective in truly organized teamfights, but if Tryndamere is having a field day splitting and your team cant get enough done in the meanwhile then it might just be worth to go shut the trynd down.
So in conclusion,,.,,,,,jax wins lane almost certainly but if Trynd manages to stall out and scale up safely then its much more even and difficult.
But they are both lategame monsters so its a battle of wits in the end, you simply have to play around his R properly.
After all, if the trynd goes full glass cannon to deal as much damage as possible to make him difficult in a 1v1 then you can easily do the same.....heck you might not even need a full glass cannon even if he does it.