i got the same choice and got the rg 370...
take the 321 man! I hate that tremolo!
-Ibanez SZ-520QM (D-Sonic/Air Norton)
-Ibanez RG-370
-ESP ltd B-55
-Engl E530 + 930/60 Poweramp
wht makes mahogony beta? sorry i dont really know the wood differences
Jackson KE 3 Trans Black
Schecter C7 ATX
Siggery Custom

Axe Fx Owner
I would get the 370DX, but if you don't have enough patience to mess with the locking trem, get the 321.

As for the bodywoods ones not better than another, they just have different tones
Mahogany has a more darker sound than basswood. Basswood is very neutral tone wood. Pickup characteristics tend to be emphasised most in basswood.

^For more info on wood.

As for those guitars, the Edge III trem which the RG370DX has is not very good.

Quote by pifty
Edge III
You will find this machine most often on 3x0 series, and lately just about everything else under the Prestige mark that Ibanez makes. This trem is ****e, because it looks okay, and feels great, looks like an updated LoPro, but is made out of an arcane mix of putty and tinfoil. Heavy whammy users report life expectancy of about three months, after which the trem becomes useless due to tuning incontinence. Edge IIIs frequently break, crumble, fall apart in ways. You should only buy a guitar with one if you are ready to do work on the machine and replace it in the future. If not, save up for a Prestige, it'll cost you less in the long run. Allegedly the EIII swaps with an original Floyd Rose.
Pros: works while it lasts, might be swapped with an OFR
Cons: manufacture quality is not there

Source: http://www.lawl.net/gtr/trems

I would personally go for the RG321MH, it's more reliable as it has a fixed bridge.