Do you have the FHLF80 already?
I have both as there are times one or the other works better than the other.
I have the F80.
There's really not much point in having both an F80 and an FH80; they both do the same thing. Being that you already have an F80, the next natural choice would be to get an FLF80 since it also has the steel handle.
If you get an FHF80, you're going to need an FH80 to match it and that leaves the F80 all by itself; you probably won't use the F80 much after that.