I'll be the first to admit I have no idea how this is going to play out. Bourjos is a quite light hitting outfielder who lacks on-base skills in his career to inspire a ton of confidence in his offense. He is, perhaps, the best defensive center fielder in the game, however. Which makes him very hard to evaluate, even with UZR.
Jon Jay, on the other hand, is definitely the better hitter... but his defense is average at best in CF. This presents a conundrum for the Cardinals, in that it is difficult to tell who to play more often. It seems pretty clear though that Bourjos has the upper hand in playing time... although Jay might be able to eek out some at bats by filling in at the corner outfield positions... but then there's Shane Robinson up in the mix as well.
Bourjos projects to get 514 plate appearances on average, which is a lot more than he's used to. It is pretty unclear what he'll do given that much playing time (although as recent as 2011 he did get more PA's than that, and put up a respectable 114 wRC+). His average wRC+ projection is 99 by the 4 systems readily available at fangraphs.com.
His average expectation for this year is a 3 fWAR player, which is pretty great. His average on-base % projection is .314, which actually matches the ZiPS projection. This is the most discouraging part of Peter's skillset. If only that were better, he would be a truly fantastic player. But still, he is better than I thought. 3 WAR is nothing to scoff at.
Another aspect of his game is stolen bases, but he's projected to only pilfer 14 this year. That is a far cry from the 40 that's been talked about. Best of luck on a great season, and upping that OBP.
Jon Jay is quite a bit different. He projects out to be a .343 OBP player, which is a bit lower than his career OBP... but still pretty great. As for playing time, his average projection is 466 PA. That's a lot of total PA from the two, but hey, it's what we have. The wRC+ projections are closer than I thought, with Jay at 103 and Bourjos only 4 points less than that. And Bourjos actually is being projected for more ISO, which was unexpected.
The fWAR average projection is 1.6 for Jay... so it seems he will be fighting for playing time this year, if Bourjos can hit some and not make errors like he did today (I know I know, it was a fluke).
Just for the hell of it, I looked up Sugar Shane, and he is basically like Bourjos-lite. Oliver projects 2.5 fWAR if he had 600 PA. Maybe some day he'll be on a team to play full time... I'm sure there's gotta be a team out there in need of a great defensive CF. If possible, either him or Jay should be traded.