I have never tried the Outlaw amps, but I have tried their flagship pre-pro. I currently own the Emotiva MPS-2.
My impression is that both Outlaw and Emotiva are very high quality. They will sound the same. I doubt that anybody will be able to tell the difference when they compare the same power-rating amps (200 watts vs 200 watts).
You cannot go wrong with either one. In the end, it comes down to aesthetics, price, and availability.
I picked Emotiva mainly because I thought the Outlaws looked ugly and costed more, which is never a good combination.
But as far as build quality and sound quality, I believe they are equal.