When Raphael was in Florence, he would almost certainly have been aware of Michelangelo’s work, but he seems to have drawn far greater influence from Leonardo da Vinci. When Raphael moved to Rome in the last months of 1508 he now joined Michelangelo, who had been working for the Pope since 1503. There is generally agreed that a rivalry developed between the two artists, but then again, this wasn’t a new phenomena in Renaissance Italy.
I think the most important change in Raphael’s artistic output was that, in Rome, he was commissioned to make larger works in the Vatican (“The School of Athens” in 1510, for instance) that also differed from earlier works for being frescoes rather than oil paintings. A whole new series of techniques had to be adopted, and he no doubt learnt from Michelangelo in this respect.