So how does RZR compare to XMR in terms of anonymity?
RZR makes no attempt at anonymity. The blockchain is as transparent to analysis as Bitcoin's. All it does hide IPs with Tor. You can already do that on your own with Bitcoin if you want -- making it automatic doesn't warrant a new coin.
The fact that authors call it "true anonymity" in their 'whitepaper' tells you enough.

P.S. These 2-page Word documents with zero details or math are making a mockery of the word whitepaper.