I don't own one, but my reading indicates that in North America DI engines are run with a rich fuel map otherwise NOx exceeds North American law. Everywhere else in the world a "lean burn" mode is used which works better in every regard except the production of NOx.
In rich mode, many DI engines tend to experience fuel dilution. I think they're getting better as ECU programming evolves. Personally, if I had one, I'd rather rig my DI engine to run in lean burn mode except on my way to the emissions test. HC, CO, fuel economy and engine wear are superior in lean burn, only NOx suffers.