I have my 14' Outlaw stored here at home stacked on top of my friend's 14' RMR... I have been around both boats a lot for gearing up, but only the Outlaw on the water.
Floor design: Outlaw's battened drop stitch is stiff and bails water as fine as any other raft I've been on. Unfortunately dirty rivers like the San Juan will build up a nice cache of sand between the drop stitch and the permanently attached floor. The Outlaw BAT floor system is a pain to work with at first, but it's easy once you've done it a couple of times.
Cleaning might take longer because of dealing with the floor, but it's not a big deal with some music and a beer. Also, the space between the floor and the edge of the tubes on a RMR is much wider than the Outlaw's. Not a big deal, but something I noticed.
handles: The RMR handles have a better grip, are more rounded so they don't dig into your hand, and are more responsive in general. Advantage RMR on this one.
Frame set up: Both boats accommodate frames easily.
Size/storage: Outlaw rolls up tighter for storage and transportation. I believe they are close to the same weight, the Outlaw is a little wider across and has slightly wider tubes. Both boats look durable, which is good if you're a less experienced oarsman and might bounce off some rocks
Performance: I only have water experience with my Outlaw so I can't speak for rowing the RMR. On the water the Outlaw has done everything I've asked it to do... punch through rapids, pivot quickly between rocks, etc. When I get a better perspective this season on the RMR's water performance I'll try to chime back in for future readers.
Both boats are great for their price points. The Outlaw's floor design is the biggest X factor with it, and I've found it works just fine and bails water just the same. My friend and I both like each boat for different reasons; we were both looking for price point boats that wouldn't compromise safety or usability, and we're both happy with our purchases.
For what it's worth, my step dad (a lifelong raft guide) is retiring his old raft and buying a new one... he ultimately decided on a 16' RMR.
Ultimately, if I had larger budget I would have gotten the RMR to not deal with the quirky floor BUT the floor works fine. It's just extra maintenance, and it allowed me to save money for other gear. Both are good rafts in my opinion and if there is ultimately some serious flaw with the Outlaw floor long term you can bet that NRS will take care of you. I haven't worked with RMR but my NRS customer service experience has been extraordinary.
I hope this helps. There's definitely some irony posting this after GreenWall's comment on Alaskans...