Meh, I wouldn't say all that.
Some former UFC fighters who went to PRIDE did all right, such as Barnett, Coleman, and Randleman. And there is the defeat of Gomi by Diaz in a vicious match in which Diaz outlasted Gomi and was able to get him in a gogoplata. There's also the Liddell KO of Overeem in the first round.
But you also have fighters like Tank Abbott, Mark Kerr, Pedro Rizzo, and Don Frye who have average to losing records in PRIDE since coming over from the UFC. Not to mention fights like Liddell getting destroyed by Rampage.
So to suggest that fighters coming over from the UFC automatically had it all over fighters who were already in PRIDE at the time is a bit of a stretch.