Okay let me give my two cents on this. Firstly, assuming that he skips all the other Gates, and goes straight to 5th Gate, I don't believe that Neji's arrogance will be used against him in this match or really at all. Even against Naruto as he still took him seriously when he pulled out KN0 and would have beat him if it wasn't for the underground technique. Especially if Lee pulls out a form/technique that he's never seen before, signifying that he's going to be fighting seriously, Neji will respond in turn moreso after seeing his chakra massively increase via Byakugan.
Next, on Rock Lee's page it states that with the 5th Gate he is likely comparable to Neji due to saving the Reverse Lotus for him, which makes me believe that it isn't until 5th Gate that they are comparable (which is backed up by the profiles). So it is in this form that Lee is actually stands a chance against Neji. Now if you take a look at Neji's speed and Lee's speed with Gates, Neji actually has the SPEED advantage (better reactions AND combat speed), while his regular speed is comparable to 5th Gate Lee's speed in general. Which means Neji will actually be the one who has the advantage. And because of this, not only will Neji be able to see through Lee, he also can counter attack with his own Gentle Fist, even if Rock Lee runs or jumps at Neji and jumps away before Neji's hits connect, Rock Lee would be the one wasting stamina- NOT Neji. Lee will be constantly losing stamina/chakra and Neji can easily see that AND exploit that.
And finally, Kaiten just easily blocks any and every attack Rock Lee throws at him so he should be able to fight just fine.
My vote goes to Neji