The probability curves on the damage differ. 3d4 is a lot more "bunched up" around the 6-9 range.
1d10+2 is flat across the board.
If I want to roll high, since I personally want a better chance for a maximum roll (even if it means a greater chance for a minimum roll), I take the 1d10+2 every time.
BTW, If I wanted to roll low, I'd take the 3d4... less chance of hitting a high number (10% vs. 1.56% to get a 3 or a 12)
But the biggest determining factor?
I'm lazy. Gimme the d10 - that's two less dice to roll and add up.
Also, 1d10+2 implies that my weapon is magical - look, ma, a +2 enhancement bonus!
I've always had good luck with 3d4, i have a matched set that rolls max or close to it more times than not. On the other hand i get burned on a regular bases with my d10's.
There you go, no math, no facts, just pure good ol' superstition.
3d4 any day, and twice on Thursday. That's when my group meets ... As the DMG notes, more randomness works against the player characters in the long run. Rolling 3d4 gives me much more predictable amounts of damage, which makes it easier for the DM to design challenging encounters which my character can nevertheless survive.
Yup, this is off topic, and you know what happens to OT polls! Anyways, the poor d12 needs more attention... it gets lonely sitting in your dice bag. Have pity on it.