There are studies showing that managers do not have as much of an influence as always thought, kind of breaking a conventional wisdom there. Then again, this does not mean that he is useless. I think basic statistical regressions can show quite a lot, yet in social sciences, one has to be careful with those regressions as there is much more a manager has to do etc. then really included in linear regression models.
I still think that Pep's influence and his leadership, rigor and work ethic was needed a lot back in 2008. Stating that world football was not as good than is kinda underestimating what this team has achieved within those years. Most of that is based on the talents one has at hand and Barca were gifted with the best players one could possibly imagine. Yet again, a paradigm in world football was broken: people tought that phsyical strength is more important than technical ability as well as intelligence. We outsmarted almost every team, including all world class teams by then, this was not only because of superb players but also because a certain kind of play was re-introduced and superbly implemented. This is due to Pep and his predecessors.
Then again, the Champions League shows that there is much more luck involved than in a normal league setting. While the league is a great marathon where really the best team is awarded with the crown, the Champions League's design is especially prone to more luck, which makes it also so exciting. If you think Pep didn't manage to win against an allegedly poor Chelsea side (Heyncke did not either) back in 2012, just check back how many chances we had to score. (Alexis, Cesc, Messi's penalty etc.)
Pep has shown to win against Mou more than one time and with different teams, he's track record 1on1 against Mou is pretty oustanding actually! Then again, it takes a lot for a manager to kick Ronaldinho, Eto'o etc. out, call the youngest player the new leader. Remember Tata being "consulted" by Xavi for a more controlled game when Tata wanted to change some things...
Pep is no saint, but he is surely amongst the top managers out there!