Thanks to everyone here (err... make that MOST everyone) for good, reflective comments on how these 'tables sound, and how they are to live with.
I've not personally owned a P3, but am very familiar with it, it being such a mainstay in our circles. I however HAVE owned a Rega Planar 2, and more recently in past years, also the MMF-5, MMF-7, and the MMF-9 (not auditioned, but owned in my system for long stretches each). Though the MMF-7 would be the keeper of this lot, for me, I've enjoyed them all very much, in different ways.
Keeping with the subject of this thread though, the Rega P3 has always sounded more forward and aggressive to me (note that I intend all of these terms in a very subtle sense), and a little more bold. The MMF-5, which so impressed me for just how much it could do at its level, tended to sound a tad lighter, certainly more laid back in presentation, and perhaps in some ways, more musical than the Rega.
But I might have used the phrase "impressed me" inappropriately just now, in trying to describe what I want to say about these two 'tables. Because overall, that phrase always seemed more appropriate to the Rega. Listening to the P3 makes music "sound impressive" (in an audiophile way). Spinning wax on the Music Hall 5 on the other hand, music seems to come out more self-effacingly; but at the same time, for that very lack of self-centeredness, the little product itself leaves an impression on you, in afterthought.
The tonearm is really the P3's sine qua non - in sound character and build quality. Overall, I've always liked the touch and feel of the P3 a bit more than the MMF-5. Sturdier and more substantial. But I wouldn't be surprised either to learn that what the MMF-5 lacks in this department actually helps it in a way, by adding to its charm. It's that "you get so much for so little" quality the MMF-5 has, I guess some psychoanalysts would find a way to show how that biases my perception of what reaches my ears.
If you've managed to wade this far through all my rambling dreck, you'll realize I'm really saying that both 'tables can serve the music quite well in their own way. That's been my experience with them. The Rega lends itself more easily to upgrades and tweaks, if that sort of thing attracts you. However, one tweak I'd suggest for the MMF-5 is a mat upgrade to smooth out the "ringy" overhanging tone you sometimes get with the glass platter.
Keep on living music.