Which is the Better Tonearm - Pro-Ject or Rega?

Which is the better arm in your opinion, the Rega 251/202 arm that's also found on the Rega clones (Edwards Audio TT1 for example), or the Pro-Ject arm found on the Debut/Essential and Pro-Ject clones (such as the Music Hall MMF 2.2).

Does Pro-Ject's carbon arm (as found on the Debut Carbon) change your position on the comparison?

The Audiomods Classic (which uses the Rega 303 arm tube) is better than either. A UK arm handmade by a designer and master machinist, whose website will tell you all about the design.
To answer the OP's question, the Rega arm is better than the Pro-Ject arm.

The Rega arms are hard to beat for the money.
If I may, can you expand upon why the Rega arm is better than the pro ject arm?  I'm doing a bit of browsing and research on both for a new TT and curious about this topic as well.
You didn't ask, but I can tell you what makes the Audiomods arm so good (especially for the price). Jeff installs internal arm tube stiffeners to get rid of the resonance peaks of the tube of the best Rega arm, also drilling small holes in it in a carefully arranged pattern, also to remove resonances, replaces the steel ball bearings with ceramic ones for lower noise and friction, machines a new one-piece yoke and bearing housing, adjusting the bearings for far lower play than even the best Rega, installs a damped counterweight of his own design, rewires the arm with either Cardas copper or pure silver wire, machines a new height-adjusting turntable mount, with an optional micrometer offered for ultra-fine on-the-fly VTA/SRA adjustment. And there are others! More details on the Audiomods website. The best buy in pickup arms.