Pretty sure replies don't even matter anymore, but this is a battle I'm very curious about myself.
Round 1: Nemesis all but stomps. Even with the G-Virus's adaptability, Nemesis is overwhelmingly more powerful than Birkin 1.
Round 2: Tough, very tough. Birkin can one-shot Mr. X in this stage, so he can hurt Nemesis for sure. But Nemesis is a seriously tough bastard even by the tough bastard standard of RE bioweapons, with only a couple of others rivalling him and only one genuinely outright exceeding him in sheer impossibility to put down. Implacable force meets immovable object. It's close, but I think Nemesis is just a bit too tough that his other qualities along with it give him the win.
Round 3: Birkin takes it, barely. Nemesis form 2 does have a mobility advantage (though probably not as great a one as it would first appear given how mobile Birkin 4 is), but Birkin 3 is terrifyingly strong by both feats and scaling. He's much bulkier and more muscular than his previous form which, as mentioned, was able to instantly kill Mr. X with a single attack: and Birkin 3 has two massive arms capable of top-tier physical feats plus two smaller, but still very bulky arms. But what gives Birkin the win is that the G-virus is still adapting and pushing his form's limits. During the fight in-game he grows even larger and stronger, and appears to super-heat his skin and claws, after taking severe damage, allowing him to move and attack faster, pause less after attacking, and flinch less upon receiving damage. Birkin will adapt to the damage Nemesis is dealing and compensate, perhaps hardening its skin or adding muscle to its legs to increase mobility (though any adaptation would involve eyes and teeth because...G-virus). With his better adaptability combined with superior physical strength, better melee weapons in his enormous claws, and incredible Regenerationn, Birkin is just too much for Nemesis at this point. Not that it will be an easy win.