I've missed everything up til now, but I want to add some possible talking points to add to the discussion. I cannot remember if we're taking, say, end-game nations or most powerful nations or whatever, but that's my fault for being an absent dick.
Given that Alexandria's summon power is pretty much vested in Queen Garnet, what are the limitations on who else from the party fights alongside them? For instance, Zidane as probably-prince would be a member of Alexandria. Vivi's kids would also likely fight, given their appearance there in the credits. Steiner and Beatrix would be there of course, and they are pretty fucking powerful.
Eiko is technically a citizen of Lindblum now (and ignoring the idea that the two would undoubtedly unite in a serious conflict), but her powers would be a huge contribution. Then you have Freya et al, who have minor connections to Alexandria and would likely have no reason to join in aside from the whole invasion from another world and party loyalty business.
ShinRa, on the other hand, has a pretty large ground force with versatile and modern weapons along with a big group of mako/jenova injected roidragers. Whether or not this takes part pre-OG (and so, theoretically, Sephiroth, Genesis, Angeal et al would be fighting alongside them) or anywhere else (post or during OG would give them use of the Sister Ray which is freaking lethal), Shinra is not going to be a push over.
They have a relatively comparable airforce - Gelnika's would probably be quite useful, and the helicopters could probably be transformed into warfare-ready vehicles too. Alexandria still probably has the advantage in the air, but only just.
All of Shinra's troops have the ability to use materia and (theoretically) this includes summons, giving them the ability to match Alexandria.
Don't forget submarines, too! Alexandria's navy has no chance there.
I dunno man. I voted Shinra but it could go either way, depending on who takes part. A lack of main party support for Shinra (Cloud and co. would likely side with Alexandria first because fuck they hate Shinra) really hurts their chances but they're pretty fucking industrious, and they did start out as an arms corporation.