Guy, I've owned and run both, but with different rigs and not side-by-side. They probably have a basic similarity about them in terms of overall tonality (on the warm to bright scale), but I'm thinking the MMP has more bite or more of an edge to it...Apogee MMP and MME owners would call that the distinctive Apogee sound...crunchy would be another adjective I'd use. The MP-2 is smooth. They're both fairly 'warm' sounding preamps.
The MMP is like a Fender strat with single coil pickups and the MP-2 is like the ES-type Gibsons (although perhaps not as mellow as a BBKing Lucille)...or perhaps an un-overdriven Les Paul standard.