While I agree that it certainly exists a rivalry between them and that Messi probably wants the Pichichi just as bad as Cristiano, I don't think that this rivarly is what drives them to score so much. Let us not forget that Cristiano already scored 42 goals 4 years ago, when he was not at his peak yet and he didn't even considered Messi as his rival. The same could be said about Messi's record in Pep's first season, while he was playing on the wing.
Both wouldn't reach this level. Not because the talent is not there, just because there would never be the need to, or more like the imagination to reach such numbers wouldn't exist. When Messi scored 25, Ronaldo wanted 30, when Messi scored 35, Ronaldo scored 40. The opposite is also true, Messi will reach Ronaldo's record soon, because Ronaldo did it, so Ronaldo will push him even further.
Yes, but at the same time if Cristiano wouldn't be RM's player, your team would have less points and Messi wouldn't have to make that extra effort every single game. And the same thing could be said if Leo would play for a team outside Spain, while Cristiano would still play for RM.
The competition that brings the best in Messi, in my opinion, is CL. You can feel his tension when he steps on the pitch or when he listens the CL anthem. Here he always gives his best and he wants to score even in the 90th minute(unlike some games from La Liga or CDR). Based on this impression of mine I also looked at the number of shots Cristiano and Messi have in the league and in the CL:
-in the league Cristiano has a shot at 12.72 min, while Messi has one at 15.85min;
-in the CL Cristiano has a shot at 16.36min min, while Messi has one at 13.50min.
So my guess is that while Messi thinks at Cristiano every time he steps on a football pitch, he also thinks at Raul or Inzaghi or Maradona or maybe even Pele. Or at the WC medal he doesn't have or at his grandmother who insisted on him playing football..or at the fact that if he doesn't score, most of the times nobody else will. All of these things, plus his natural talent and love for football made him the competitive beast that he is today.