I am a Pro-ject guy having had a RM 1.3 and now an RM 5.1 SE. Never had a Rega so I cannot do a direct comparison. I can only say I like the Pro-jects very much, nver had any roblems with either table I've owned, and feel they are outstanding values for the money.
That being said, if you budget is $300 for a table & arm without a cartridge, then look at the new Pro-ject Carbon at $400 with a cartridge! It is a souped up version of their already best selling Debut III having the following upgrades - 8.6" full Carbon Fiber Arm, RCA jacks for your choice of cable, full 12" platter and factory equipped with the Ortofon 2M Red, a $100 cartridge that I believe was already recommended in this thread. In the $400 range for a table & a cartridge, Pro-ject appears to have a winner here. Hope this helps.
Parasound 5125, Parasound 2100, Pro-ject RM 5.1SE, Dynavector 10x5, Pro-ject Phono Box S, Pro-ject Speed Box II, Arcam FMJ CD17, Pioneer Elite VSX-52, Pioneer Elite BDP-52FD, Vienna Acoustics Bach Grands, Vienna Acoustics Theatro Grand, Wharfedale Diamond 9.2s, REL T-1 & Panasonic TC-P54S1