Of the three, I now only use ES File Explorer! It works perfect over Wifi connecting to my LAN computer/server. I haven't yet needed/tried any of the other methods of file transfer, but knowing that they are there is reassuring.
When I was first exposed to android, the Astro File Manager was THE app to use, but somehow I got more confortable with ES File Explorer.
During my first tablet exposure (ASUS TF101), it appeared that File Manager HD was the preferred app, but again, I migrated back to ES File Explorer.
The only thing I do not like about ES File Explorer, is that ALL the commands are in a menu and none can be relegated to a button (AFAIK). Even a "redo the last command" button would be appreciated.
Since they are all free, why not install them all and try each out. Then uninstall the losers....