Jax. I won't bother pushing Nasus out of lane I will just also scale very highly.
And you'll lose. Jax vs Nasus is a win for Nasus even if you try to murder him. Wither is too good at neutering jax's DPS (just like Malphite's E is) and will effectively stop you from murdering his carries when team-fights come around. Jax's E doesn't block Nasus's Q (found about that the hard way unfortunately) or his ult (but it does reduce the damage obviously), so he can 1v1 you post-6. You get whacked with Q for a ton of damage, deal not a whole lot to him as he withers you and has glacial (or at least a chainmail) oh and he ults for more damage also getting more HP. Did I mention he has sustain which does apply when he uses Q?
The only way you could win this is if the nasus is dumb and you manage to get a kill very early and snowball.
Wow Nasus must have carried you to 2500 elo if you're this good.