It isn't uncommon in Australia or New Zealand to see a Rugby Union player change codes and try their arm at the more lucrative Rugby League. It is, however, a bit more uncommon to see a League player convert over to Rugby Union.
The games are so similar, yet so different. They require similar skills in the way you run, pass, and kick the ball, but the way you use these skills varies between the two codes.
Rugby Union is a lot more technical than League, which is where most converts find they struggle. They find that they're unsure when to commit to the break down and when to hang off. They can also be a bit "brainless" at times, trying to do fancy things that they might get away with in League, but in Union they are scorned for simply trying it.
This article profiles five of the most successful players to convert from Rugby League to Rugby Union. There haven't been many who have done it successfully and it was hard filling the last few spots, but I think this list is a good representation of the most successful converts of all time.
Just a footnote, I decided that in order to qualify for this list the player had to have played at the top level in both codes. For example they might have played NRL and Super 14 or Super League and Heineken Cup.