Can't think of anything that would affect you as an American. The AG structure has a load of requirements in terms of worker/trade union representation on the supervisory board (typically 50% employee, 50% shareholder). The SE structure & relevant laws look very similar to AG, but allows/requires equivalent employee work council representation from across European rather than just German employees. For shareholders, there's basically no real difference. In theory there are advantages to not having to worry about ~30 different lots of European company laws, in practice, AFAICT it has made no difference.