I consider rescue hook-type line cutters, safety cutters. You have to orientate it a certain way to capture the line and make a cut. This makes it less likely to cut yourself but it can also be troublesome since you can't just dive in and cut from any angle. With a knife, your attack angles are less limited. If you want heavy duty cutting capabilities, you rely on EMT Shears.
Don't get me wrong though, for cutting monofilament, most of them work much better than plain edge knives. Their equally as good when compared to serrated knives.
However serrated knives hold an edge over shears and rescue hooks when cutting rope. You can also pry and dig a little bit better with a knife, although those situations are specific and far in-between, for me at least.
My usual knife of choice is a Dalton (DIR) Safety knife. It's basically a sawed-off serrated steak knife with 2inch of blade rounded off at the end. Very small and easy to work with as opposed to some of the bigger knives out there.
The usual sheath is just a 17in piece of webbing folded in a Z-pattern and then stitched/glued. Fits on any 2in webbing belt/strap, friction works to keep the knife from slipping out. And it does an excellent job in that regard.
Best part is you can make the pieces yourself using files, bolt cutters, and your neighbor-hood cobbler. I'm in the process of finishing some up myself. I can give out the instructions if you want.