So...10 and 4? I'm not entirely familiar with his feats up through his 4th incarnation, but his collective feats up through and including 10 are as good as any in comics.
It's really, really too hard to call these kinds of fights. In a forum setting, you're looking at universe-busting power (or greater) on at least the Doctor's side, and probably both sides. We can't fathom that kind of energy, much less how it would interact. The Doctor is probably the most plot-devicey tech and prep god in all of fiction, and I say that with full awareness of comic silliness in these realms. But everyone has limits, and it's more than likely this would end in some sort of stalemate or mutual annihilation.
Safe to say it could go either way with teams like that. And like someone already said, could quite easily end up in universe busting mutual destruction or a stalemate.
But I would have a feeling that with the usual plot devices the fourth Doctor has a chance of coming out on top somehow, add in the tenth as well...
So if I have to pick one team here I think team 1. Maybe it just comes down to Doom being a villain and Thanos always losing in the end.