Meh shino...Shino's only been shown in 2 1/2 fights in the manga. one in chunin exams, where he didn't have to hide at all. 2 with kankuro, where he was able to utilize his surroundings. and 1/2 fight against tobi where he also didn't need to hide. it's probably agreeable that he does work better in forestation but he does well in the open as well. even on the battlefield, he calmly kills zetsu's like they're nothing.
against neji, logically, neji would surely run out of chakra first. no chakra for neji = a lose...
1. shino's bugs would most likely tank an air palm
2. amazing speed feats. just because neji can see the bugs doesn't mean he has a counter for them all the time
3. neji's rotation would be useless, since shino's bugs are living creatures and not normal elemental ninjutsu. therefore, the bugs could easily avoid the rotation by simply hovering until the right moment to strike.
4. this fight would be much harder than fighting spiders because shino's bugs are way smaller in comparison to the spiders, so it's highly unrealistic (and if not unrealistic), extremely taxing for neji to palm every single bug. Shino also has an advantage that he doesn't tire from fights as quick as others because he may use such little chakra. Neji would surely tire first because he is mainly close range, which shino knows.
5. since neji is also a sensory type ninja, shino could very well use a few insects to "fog" neji's byakugan vision, thus forcing neji to focus more chakra into his vision. in turn, it A:...consumes more chakra B:...splits his attention C: provides Shino with yet another distraction
6. also, it doesn't show anywhere that neji uses any other tools other than kunai
so in fact, i believe this is a bad match up for neji as well. Shino would win more times than he would lose. i'd say 7/10 wins for Shino