In the databook they may be tied at that point in time, which was when the series had started, but Neji during the war was much better and stronger than at that time. And even then an argument could be made because his experience in taijutsu, knowledge of techniques, jutsu, and style are very different from the standard taijutsu that most ninja like itachi would use.
Nejis speed feats are actually pretty impressive himself. I couldn't really be bothered to link all of his speed feats, but it is enough to say that neji is no slouch in the speed department. Plus he trains and is able to keep up with people who are faster than him on their feet like guy and lee. Shuriken will not be a useful factor considering that neji is skilled with them and kunai, has trained with a weapons master who has perfect accuracy, and is also capable of defending against a barrage of them if necessary. Though his ability to read his movements will allow him to keep up with neji, neji's handspeed is second to only gai's morning peacock and will eventually allow him to land a few blows which will lead to his inevitable defeat in CQC.
Precog would make up for gaps in natural reactions, but not experience and knowledge in taijutsu itself. Neji knows how to attack and when to attack, and when he does, every single one of his attacks are precise and calculated with no wasted movements as observed by many people, allies and opponents alike. Plus, because of his techniques, he can easily gain the upper hand in a fight, and with his renowned taijutsu style, neji is capable of decapacitaing or even killing a person with a critical attack to a vital area. There has to be literally be no mistakes when fighting an high caliber taijutsu fighter such as neji in CQC.