Here is a direct quote from a Brownell rep explaining the different aspects of Fury and Rhino:
FURY --> This is our Top Shelf, high performance string material. It is not a blended product so there is no Vectran, it is 100% Ultra High Weight Molecular Polyethylene (UHWMPE). We had people asking for a micro diameter string material that pushed the envelope for speed, stability and something that offered a soft shot. After. many samples run and some fine tuning of material we ended up with what we now refer to as FURY. The most exciting thing for myself as an archer was the stability of the FURY. Not only does it settle in very quick once on the bow, it doesn't move after that. We tested FURY in every weather situation possible, super dry hot heat, super humid weather, ice cold New England weather..... You name it the FURY was in it and it still never budged. To have a material that does not change at all in difference climates was key, this is what shooters need especially shooting ASA and IBO tournaments where the weather is always changing. Take for example the Florida Pro am this year, uncharacteristically cold at the beginning of the tournament and ended with 70 degree weather. Also take into account that Tim Gillingham won, shooting FURY!!!
Besides its stability FURY has been reported by customers and consumers to be a contender for one of the fastest materials out there. I'm not going to dive too deep into the speed battle since there are far too many variables to argue one material is the fastest out there. However I can say that our builders and customers have seen FURY to increase speed more often than not.
On top of the stability and speed that FURY offers it also offers a very soft, quiet shot as well as makes a killer looking string. Most of the time the first thing a string builder or consumer notices about their FURY strings is how smooth and shiny they are. Part of this is the material itself, but I also think some of it has to do with the small strands which allow the color bundles to pack together tighter once burnished.
Rhino --> Rhino has been adopted by a lot of shops as the go to all purpose material. Rhino was originally developed as a crossbow string material because of its very high strength (averaging 130 lb break per strand), and its lack of creep on Compounds as well. Once it was sent out to some of our customers we had a huge influx of Traditional Bowyers and shooters start ordering the Rhino because it was working so well as a flemish and endless loop string material.
Hope this helps!