requires attack speed to do damage. Anyone who can ruin his attack speed is gonna give Jax a hard time. You say late game 1v1, so I suppose a late game Nasus would simply annihilate him. Let's see why.
has a point and click movement and attack speed slow. Jax can build
,
,
or
this, but that means he must kill a Nasus in a matter of less than 6.6 sec, as Nasus's Wither would be up then (assuming 40% cdr). This is potentially doable for Jax, but he can only dodge 2 Siphoning Strike at best under his 2 second duration Counter Strike, that is if the Nasus is dumb enough to attack him then. Once Jax's Counter Strike is done, it won't come back to him after another 4.8 seconds (assuming 40% cdr), when Nasus's Wither would be up. By then Jax has the choice of Leap Striking out of the fight, because there is no way he can deal with Nasus's infinite scaling, especially when Nasus is under his ult, which reduces his Siphoning Strike from 2.4 seconds to 1.2 seconds. On top of that, Jax has to deal with a tank Nasus, who will build both armor and magic resist to deal with Jax's hybrid damage. Jax has no innate armor or magic penetration. This means that Jax has to get some form of armor or magic resist shredding item, like
(prob his best choice),
,
,
or
, which means Jax would be building more squishy (Wits End offers mr which will not help tank against Nasus's Q, and really Black Cleaver is the only one that can give Jax some defense, especially with his ultimate's scaling). Even if Jax goes semi-tanky (pure tank Jax will definitely not win against pure tank Nasus) and/or uses his ult, he will still take a good hit from Nasus if he doesn't dodge his Q, because Nasus's Spirit Fire allows him to reduce 35% of his enemy's armor. Jax could buy a Zhonya's or Guardian's Angel to buy some time for his Counter Strike to be up again, but they will not add much offensively against tank Nasus. In the long term, we know that Nasus's dps will outscale Jax. Jax has some disgusting stats (88% attack speed boost, even worse if you mix that with Lethal Tempo), but a capped stat simply will not outscale an infinite scaling ability.
Also, here are some good champs who can deal in a 1v1 with late game Jax pretty well.
, and to an extent
(Rhaast).