Sasuke was cooler and Neji was stronger than Sasuke up to a point but I think he can beat Sasuke. Neji was still standing after fighting initial Cloak mode Naruto. Sasuke fought a stronger Initial cloak mode Naruto but Neji did get stronger himself so we can put Neji on that level which isn't too far power wise from CM lvl 2. Sasuke was in a coma for about 4-6 weeks I think but Orochimaru pill did increase Sasuke's base stats as it gave him CM lvl 2 so that made up for Sasuke being out of commission as Neji and others trained.
Sasuke used Lee style taijutsu which Neji knows about and have beaten. Neji showed that he can fight opponents faster than he is with his Byakugan by fighting Naruto in his Initial cloak mode. Kakashi himself even said he thinks Sasuke is no match for Neji when he saw Neji fight Hinata
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and Lee believed Neji to be the strongest genin
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Yes I know this is before the month training and is both are stronger by the end of the manga but I think it's important to look at the gap in strength they had at that point then we see them both get stronger in a month time; Neji could take on Naruto's base and his Initial Kyuubi mode but lost because Naruto unique strategy but it should be noted that Neji wasn't fighting in a death battle and if he was he wouldn't have deactivated his Byakugan at the end. Naruto in base was about to beat Sasuke in the rooftop about a month (or a week or so over a month). In the time Sasuke was in coma, Neji and Naruto were training (using Naruto as a way to try to compare the other two with each other) with Neji improving his skills with gentle fist, chakra control, and learning more Hyuuga clan jutsus and Naruto trained in chakra control and learned Rasengan.
After Sasuke got his stats increased from Orochimaru pill, his base was stronger than Naruto's base and had to go initial cloak mode to get the edge in the fight but Sasuke went CM lvl 1 to get the edge and it went that way until they were at their strongest. Sasuke doesn't just got full power in part 1, he levels up when he needs it so Neji can get it blows with gentle fist or setup the 64 palm which can kill Sasuke.