Well, both are accepted here, that's for sure. I'd say there is a difference though.
"znudzony" describes a feeling. You feel bored. Something made you feel bored.
"nudzę się" is... well, not an action, but something that happens with you. You are bored, you have no idea about any interesting thing that you could do to stop being bored.
Does it make any sense? I don't know how to explain it better. If it doesn't, then I guess it's just safer to go with "nudzę się" every time.