I have owned both the P3, P6, and 1200GR (original Japan model), though no two at the same time. The Rega and Technics are very different animals with differing sounds and feature sets. The feature set on the 1200GR is stellar. If you play 78s and 45s, as I do, one just needs to push a button and the universal headshells allow a quick switch of cartridges. Speed correcting off speed 78s is also easy, or default to 33 and the quartz lock is right on.
Regrettably, I did not care for the sound quality with a variety of cartridges. Lower midrange and bass, to me, and in the context of my system, was always thick and confused. I was never able to get it sounding acceptable to me, YMMV.
The P3 is a stripper as far as features go and changing 33 to 45 is inelegant. That said, I could easily live with the direct and resolute sound quality. I will also say that I am not saddled with perfect pitch. If I was I might have a different preference. Good luck with the hunt.