For his career, Branyan has hit for a .790 OPS in 900 plate appearances. As a Red, he has hit for a .900+ OPS in over 120 plate appearances. That improvement in his 120 PA can NOT be shrugged off as random noise in the data (or as a small sample size for that matter). The difference between his career numbers and his 120 PAs as a Red is likely STATISTICALLY SIGNIFICANT (caveat: I don't have the software with me to run the numbers
Moreover, Branyan's hitting has improved across the board--hitting for a higher average, fewer Ks, more walks, higher slugging percentage, etc. That is further evidence that we are witnessing REAL improvement in his performance.
Add in the fact that he has always had a ton of talent (top prospect in 1997-1999), and this is likely a case of where a change of scenery has done a world of good.