Well, since I've been an admin for both AMX and adminmod, I'd say rcon rules all sicne you don't gotta' install anything, ha ha!
On a note of seriousness, much like xJ said, AMX is mostly for the more popular fy_ maps, awp maps, and also has a lot more plug-ins available for it. As far as admin commands go with AMX, you get mostly the standard stuff, amx_kick amx_csay amx_tsay amx_ban, and it has a nifty easy-to-use menu you can access by binding a key to 'amxmodmenu' in console, which makes everything
much easier.
Admin Mod has mostly the same commands, but once again, like xJ said is mostly for servers which don't play fy_ or awp types maps, mostly for regular maps, as admin_mod doesn't have a neat little menu, at least as far as I know, and it doesn't have the felixability that AMX does. It's built for the basics, kick, ban, and a neat little function the server I play on uses called admin_llama, which basically truns a spammer into a Llama (Changes his name), and every time he types it says 'Ooorgle!' ior something similar. very funny to atch these people start shouting at you on the mic because they're spammers.
So, choose accordingly.
-Frank
