Kabuto Yakushi is the Main Brawler on the Akatsuki-Side of the War. He is relatively closely followed by Obito Uchiha however the two can be debated and interchanged. I think that Kabuto is the Main-Driver for several reasons. The first of which is Edo Tensei. This jutsu was used in miraculous ways during the war.
First, it opened up various fronts against the Allied Shinobi Forces and it could be debated that the White Zetsu Army killed more people but it is indisputable that the Edo Ninja were more effective. It brought various divisions together and killed more ninja in terms of ratio. Again, you could argue that the Edo Ninja like the Zetsu Army only killed "fodder" ninja and nobody special. Obito/Madara did that. However the deaths of these so-called fodders destabilized portions of the whole fighting force and killed the will of some ninja. Neji could be considered fodder in comparison to Naruto and Obito - his death almost made Naruto lose his Will of Fire and made him want to join Obito.
Second, is the fact that he dealt with Itachi Uchiha and the inclusion of Madara Uchiha in the War. He is clearly not the strongest of shinobi but he is easily one of the ten most powerful ones and on the Allied Shinobi Side of the War, the second strongest force to be reckoned with. Madara wiped out an entire division with Shingei Tensei rendering a devastating blow to the Allied Shinobi Forces. He then went on to defeat the Five Kage.
The last part are the Edo Jinchuriki. Without them, Obito Uchiha wouldn't have been as intimidating. He was able to fight Kirabi and Naruto and later Gai and Kakashi so formidably because of them but you could argue that he lost a lot of chakra because of them and couldn't have done much more without them as well. However, from what we've seen, you could say that Obito would've lost without them. Also the Jubi wouldn't have been summoned without Ginkaku and Kinkaku and we all know how powerful the Jubi is. Madara would be fighting the Edo Hokage, Naruto, Gai, Kakashi, Kirabi & 40,000 Other Ninja. He is not winning that battle without a force like the Jubi.
Kabuto was pivotal to the War lasting So-Long.