Seeing as there is a veritable sh*tstorm on the forums about the new ranking system, I have decided to do some constructive discussion on the new patch about the state of Tryndamere.
So before the patch I was looking for a strong top and I was trying out jax, but failing horribly, so when the new patch came out and I saw Trynd was buffed, I decided to play him. I've managed to snag top three times so far this patch, and all three times I was "countered" by jax top. (And one really fail trynd jungle game - he still sucks at jungle)
I won all three games.
Now I know, I know, three games isn't exactly a strong measuring stick, but since I was playing Jax before the new patch, I realized a few things about him that allowed me to play trynd against Jax reasonably well, with and without ganks.
The first thing is that Trynd has pretty good sustain against melee types like Jax, because he can just hit hit hit and build up his rage, which gives him a (at 100 fury) 80 hp heal every 12 seconds. Now this may not seem like much, but keep in mind that a pot gives 10hp a second, and this isn't that far off, so this is basically a pot that is always on. Now, this only applies when you can keep your fury at 100%, but if you're playing against Jax this shouldn't be a problem.
The second thing to realize is that while jax has the whole "counterstrike" thing going on, his whole base movespeed is shit, so you can just walk away from him and not get stunned. Even if he jumps to you, you just spin away, and then walk right back to him and start slapping him with your giant-ass sword. What I like to do is take a couple of levels in spin so the cooldown matches cd on your heal, which is pretty useful, you can just spin and heal, spin and heal.
Finally, Tryndamere deals damage based on critical strike, which lends itself to a more damage oriented build. On the other hand, Jax's build leans more towards a tanky build: His passive takes time to stack up and his ult procs on every third hit. This means that the initiative is yours, which is a really sutble and useful trait to have in ganks and avoiding ganks. When you spin in, jax is going to WANT to fight you, he needs time to build up his passive, and his stun isn't instant. On the other hand, if he jumps you with his stun ready, you can just spin, spin, spin away, heal up, and go back in. Meanwhile, Jax has a pretty fricking low mana pool and just wasted his mana on a useless move.
In conclusion: Jax isn't that good of a counter to Tryndamere. He is both outsustained, and outmaneuvered by trynd and trynd has the advantage of intiative. Pick like jayce or rumble instead. Maybe singed.