PECOTA and CAIRO are basically dead even on the offense. They're projecting 917 runs and CAIRO says 916. The big difference is the runs allowed. CAIRO says 695, PECOTA says 789.
Here's how the pitching projections differ.
cIP: Projected IP in CAIRO
cR: Projected runs allowed in CAIRO
pIP: Projected IP in PECOTA
pR: Projected runs allowed in PECOTA
dIP: cIP minus pIP
dR: cR minus pR
The CAIRO IP are based on the last set of Diamond Mind simulations I ran, averaged over 100 seasons so they don't line up with what the CAIRO spreadsheet, and they need to be tweaked further. I didn't realize Burnett was only pitching 167 innings, for example. However, if you look at where things differ, it's primarily with Burnett and Gaudin in terms of rate of performance, and then in how many innings they're allocating to people like Boone Logan and Jonathan Albaladejo.
Digging a little deeper into what these numbers say, PECOTA isn't displaying total runs allowed so I divided the total 789 runs allowed in their standings by the 673 projected earned runs on the team depth chart to reverse engineer it. Right off the bat this looks off, because the ratio is 1.172. The typical ratio is generally 1.08. In fact, this is really, really, really screwed up. Since 1946, there have been 1507 team seasons. I'm using that cutoff to remove the small glove/ deadball era and the WWII era where you had players who didn't belong in the majors to get closer to the modern error rate. In those 1507 seasons, there have been 59 teams that had a RA/ER ratio that high or worse. So they're either predicting the 2010 Yankees to allow unearned runs at a rate that has happened at a rate of 0.03915063 in the MLB team seasons since 1946, or they screwed something up.
They have some smart guys over there, so my guess is it's the latter. As someone who screws up his spreadsheets constantly, I can understand that. I left a comment over there asking for them to elaborate. So don't worry about these yet.