I have after long time playing come to enjoy every race and build, but the race I feel closest too is the Orsimer.

Thus I thought it would be fun to ponder, which factions victory would best benifit Orsinium and the Orsimer race?

Empire, as it was only by imperial decree (forced by Orcish possession of the Numidium) that allowed Orsinium to exist as a territory in relative peace. If the provinces return to existence as sovereign states, you can bet that Skyrim will join Hammerfell and High Rock in conquering their lands.

From the orcs I've spoken to, orcs that leave the Stronghold tend to join the Imperial Legion, and the empire readily welcomes them, because of their fighting prowess and their smithing abilities. In general, the empire has been the best thing for the orsimer.

Not sure how the Stormcloaks/Independent Skyrim would view them, but I could see the two having a very easy time getting along, as they're both very similar.

And yet many of Ulfric's people (especially in Windhelm) are bigots. I forget who said it, but someone said how Ulfric doesn't care about non-Nords. How there's s murderer running around in Windhelm killing dark elves and Ulfric doesn't life a finger because no Nords have been killed yet. So to answer your question: the Empire is better for them.

Ulfric himself (and his right hand) don't mind them joining the Stormcloaks, so long as they want to see the empire fall. I will say it would probably be more beneficial for them to join up in the legion, but I'd imagine acceptance would come to the Orcs much easier than any other of the Merrish races. Nords tend to respect valor and honor and combat, something that would probably come marginally easier than a Dunmer. I'm reletivly certain Nords and orcs have banned together a couple of instances in history.