I've used both on Sport track, and would imagine the differences are similar for Carrera.
The biggest difference will come with tire prep. If you just run them out of the package, they'll both have excellent grip.
NSR tires, however, benefit greatly from two things. First, treatment with NSR tire oil. Once that has been fully absorbed (a few hours, so best applied AFTER a race night), and just before a race, you clean them with lighter fluid. I have no idea what chemical process occurs, and it only seems to work on NSR tires with their oil, but the result is amazing the first time you see it. The shinyness from the cleaning stays. It looks wet, still. The tires have more grip than any other tire I've used. Touching them feel like they might be sticky, but they're not. It's crazy.
As they get dirty, they lose grip, but that depends on how dirty the track is. Cleaning them again will bring back the grip, but less and less each time until you re-oil them.
If you prepare the NSR tires as above, there is no other tire I've seen that comes close to the level of grip they have on any track short of putting actual glue on the tires/track (a-la 1/24 commercial cars). If you don't, then they probably end up about equal. I would probably give the Ortmanns the upper hand because urethane in general deal with dirty tracks and tire wear better.