Shino actually stands a fairly good chance.
He's just as good short-range as he is long-range. It's a bad idea to get close to an Aburame. Least you get swarmed and can't escape. Assuming Neji tries to make it close-range, he gets close and he's at a risk from being an easy target.
Insect Sphere is an effective move for Shino to use against most opponents. The insects refuse to allow their target to escape, covering a wide range of the battlefield and halting the tiniest movement when their target is caught. Insect Sphere is difficult to avoid.
Eight Trigrams Vacuum Palm has a specific target rather than a general area. That means it focuses on one point only and as explained before Insect Globe focuses on the whole area. Neji is going to be able to blow away one area of insects but not the rest surrounding him.
Revolving Heaven won't work if Neji is physically restrained and thus unable to spin. If he notices the insects and rotates them away, it'll be effective. But Shino doesn't fight by making his insects obvious. He distracts his opponents away from the bugs in order to have them overwhelm the opponent, so if Shino somehow manages to get his bugs (the Kikaichū happen to be very good in ambush) to swarm Neji and restrains him, they'll halt the tiniest movement and making it impossible/difficult for Neji to spin them away.
On the other hand Blow Body might be effective in allowing Neji to escape. But there are two things to consider: once captured the insects immediately start feasting on the opponent's chakra. While Neji would be able to use Blow Body to escape, he'd have less chakra. The second thing is that the insects don't allow the opponent to escape.
If the Kikaichū capture Neji again and drain more of his chakra, repeating the capture by insects and escape by chakra blast, Shino could gradually tire Neji out.
Just to confirm, I'm only stating Shino has a good chance of winning (and that it's not so one-sided on Neji's part) and explaining my reasons why I think so.