The alliance would win.

If bringing an ally is allowed they would still win.

The UNSC was able to fight a 25 year long conflict against an enemy at least as powerful as the reapers by itself. The entire Mass Effect galaxy combined was all but defeated in roughly a year.

Do you really want to elevate the Covenant to a Reaper-scale adversary level?

Still the UNSC got their asses kicked on almost every theater of war and even got lucky that 117 found said Halo ring in the first place and the realisation that they needed a human to interface with the forerunner tech prevented the Covenant to simply glass Earth in Halo 2. Correct me if I am wrong.

If you ignore the psionic potential of biotics and the impacts of the Mass Effect physics itself, then the UNSC would not just be on par, but vastly outnumbering.

As the whole Mass Effect universe is build on said Mass Effect physics, the Alliance would counter that. A Sentinel or Adept would fling a Spartan up in the Air and the Mass Driver Weaponry would shred the UNSC Vehicles and Gear into pieces.

The UNSC uses slipspace (hyperspace), thus being able to use outmaneuvering tactics, though the FTL-Drive works similar and is more easily to use.

It's apples and oranges in the first place but I'd bet my money on the Alliance.