The main forces from them Matrix universe are the Sentinels and the Bombers. These things have guaranteed victory for the Matrix before but here they have finally met with formidable resistance. Bascially I think that all the heavy hitters from the Inuyasha universe (Inuyasha, Sesshomaru, Naraku, Kagura, Yoga, Miroku) can handle the sentinels no problem. The human rebels from the matrix universe are no match for the various demons from the Inuyasha universe. This only leaves the bombers, which would saturate the battle field with those intelligent bombs. Taking these out will require finesse and cunning. I think that Inuyasha can take out one bomber at a time with the Wind scar attack of the Tetsaiga. I am pretty sure that Kagura's control of the wind will allow her to take out the intelligent bombs. I think that maybe Miroku could suck some of them into his wind tunnel, but he probably has a limit. As long as one member of a universe still stand that counts as a win. Miroku's wind tunnel may not be able to handle a lot of bombs and therefore it will crack. A crack in his wind tunnel will result in it sucking him into it along with stuff around him. So he will take out the bombs one way or another.
The Matrix itself will not play a role since I don't think the members of Inuyasha's universe will be capture, let alone be subdued enough to be hooked up to the matrix.
Winner: The Inuyasha Universe