As already described in the wiki, Mamba is an outdated alternative to Cobra.
Cobra itself is simply a payload that adds some features to the ps3....and most of these features are built into HEN as far as I know (except PS2 ISO support).
HAN, Hen, and HFW are more or less the same thing:
first was HAN, it allowed us to tinker a bit with the console. At some point HAN went HEN, with increasing capabilities. Sony patched the browser exploit which was used to apply HEN, but then Habib (4.84.1) and Joonie (4.85.1) created their own firmwares with the exploits available as HEN entry points, named them HybridFirmWare, or HFW for short.
if you don't have the possibility to use a permanent cfw, the choice will fall on hen anyway ....which, as already mentioned, has the most common features that a standard user needs