MC-E Max. current 700mA
P7 Max. current 1000A
Both are rated at 7000mA per die.
The P7 is hard-wired with all four dice in parallel, so it is rated at ~2.8A at ~3.3V
In the case of the MC-Es, the dice are independently addressable. This means that the user can choose to wire all four in parallel (like the P7-- 2.8A @3.3V), or run 2-series, 2parallel (1.4A @ 6.6V), or all four dice in series (700mA @ 13.2V) In many cases, series-wiring works out to be a lot more efficient, especially in cases like fixed lighting projects, it's a lot easier to find DC adapters that output ~1amp at ~15 volts, than ~3 amps at 5 volts. The option for series wiring, as well as the availability in warm- and neutral-white colors is the main reason I personally prefer the MC-E.
A few other differences, the MC-E's dome is the same diameter as the aluminum "ring" on the XR-E. This means reflector and optics that could fit the XR-E will also fit the MC-E (I have use tri- and quad-optics like
these from DX successfully with the MC-E).
The P7 is much larger. this means it won't fit in small reflectors. However the larger dome does have its benefits. The apparent die size is somewhat smaller in the P7. This means the beam from a P7 will be more concentrated (better throw) than an MC-E used in a similarly-sized
large reflector. Also, the dark "+" shaped void in between the four led dice is also somewhat less apparent with the P7 for this reason, so P7 is better suited for use with simple aluminum reflectors, like say throwing into a Maglite head. For the MC-E I'd recommend using TIR optics (like the plastic ones I linked to) or heavily textured reflectors to mask the dark void.