Perhaps we can actually have a meaningful discussion of the merits of Bush and Meche without all the NL-AL nonsense.
As I see it, Meche has two advantages over Bush, and Bush has one over Meche. Meche is more durable (more IP/season) and a somewhat better strikeout rate. Bush surrenders fewer baserunners and also has the benefit of being somewhat younger. The difference in career pitching numbers averages out to zero with an infinitesimal edge to Meche. If they faced off when all else was equal, historical Meche and historical Bush would probably split a 100 game series something like 52-48 in Meche's favor. It's hard to say, though, since that kind of dynamic will never really be put to the test. There are way too many dynamics in baseball for ALL else to be equal.
The other dynamic here is that Meche has really improved over the last couple seasons while Bush has not. It's very possible going forward that Meche might be the better option as a result. Meche's improvements are largely a result of greatly reduced bb/9, which doesn't signify a whole lot but might mean that he's got his stuff together and finally "got it." On the other hand, Meche's bb/9 is back up to his career levels this year at 3.6 per 9, so unless he goes on a hot streak, the ugly word "regression" rears its head.
For a fifth starter, though, either option is more than adequate. A durable, league average pitcher for a #5 is a good way to go. Meche might be a little better but either pitcher should get the job done.