There's no reason to expect any difference in performance.
In my opinion, the ternary operator should only be used if all three operands are very concise and easy to read. Otherwise I think it has the potential to make code harder to read.
I think a lot of people mis-use this operator by jamming too much logic into one long line of code. I personally won't use it unless the whole line is less than about 80 characters.
Good:
return isFunky ? funkyValue : null;
Bad:
return (thisThing == thatThing && (anotherThing != null || ! IsThisTrue())) ? someThing.GetThis().GetThat() : yetAnotherThing.GetBlah().GetFoo();
I've seen people do a lot worse than the above. I think they should loose their ternary privileges!