For desktop mediabox use, I like Ubuntu flavors. Though, I personally would stick w/ their LTS (Long Term Service/Support) releases. Their last LTS release was 10.04.
I don't use GUI for moving files about much. I find it to be a bit... restricting. I normally drop to CLI/shell for file management, possibly because that's all I use at work.
Rather than use "mv" for moving files, I normally opt for "cp" to copy the file (cp -R /path/to/original/files/* /path/to/destination/folder/ to do a recursive copy of files and folders), especially if the data is from one physical device to another, because this will retain the original file for me to verify data integrity before removal of the original.
About the only thing that would prevent you from copying/moving files to a destination is if the destination doesn't have appropriate permissions/ownerships to allow you to perform this task as the user you're performing the task as. However, if this is the case, you would ~normally~ receive feedback stating you do not have the necessary privileges/permissions. CLI/shell does this w/o a doubt, GUI should do this too.
Anywho, if I try something in GUI and it seems to fail for no reason, I usually drop to CLI/shell and try again, because sometimes the GUI configuration could be masking/hiding errors/messages in an effort to be "neat".