What is the better sounding turntable: Project 1XCarbon or the Rega P3 ??

First there is a differences between turntables . The problem is you can't detach the sound of a given turntable to a particular tonearm as you can't detach the sound of a particular cartridge to the tonnearm its mounted on . 
In other words, its a system .

That being said the tonearm that comes with the Rega is excellent and would not be out of place on a turntable twice the price of the P3 . Now at this price level apart from the excellent Rega tonearm there isn't much difference between the turntable plinths . Both have more or less the same isolation capabilities and their bearings are of comparable quality . 

If your going for the long haul and not upgrading in the future go with Rega . If you visualize yourself latter on upgrading into topnotch turntables go with the least expensive . Im sure the project will be.more then capable of giving you musical satisfaction till you upgrade . All projects at their respective prices are very competitive .

Be happy and just listen to your music and enjoy...stop think which is better,god forbidden you pick the wrong tt....relax ,just enjoy the music....don't worry that the other brand you read sounds better than yours....STOP IT....all your going to do is drive yourself NUTS.

@sunnyjim ,

@limomangus is right.

At this level there’s nowhere enough difference to worry.

Some really good words of advice there.
Certainly worth a screenshot.

I'd go for the Pro-ject, easier to setup with different cartridges.