Aside from the obvious point that any correlation between uniform change and improved performance does not equal causation, and understanding there's a lot of whimsy here...
Most of the times teams change uniforms to signify a new era and put the past behind. Typically, that is a past with little or no success. The only team that might be considered an exception is Denver. They had made 4 SBs with the orange shirts, but of course they had lost each time. So even there, the ultimate success had not been achieved and the uniform change was made perhaps to help change the psychology of the team (and forget the loss to the Jaguars in the playoffs).
But in the case of NE and TB, these were franchises with basically no history of success. The high point of the red-shirted Pats was SB XX and a 46-10 defeat. Six seasons earlier, the Bucs had been shut out 9-0 in their only NFC Championship appearance.
Both teams successfully changed their performance for the better, but I'm going to go out on a limb here and suggest that changes in the team's fortunes had more to do with first better coaches and GMs, followed by better players. In other words, Tom Brady and Bill Belichick (and earlier Bill Parcells) have been more responsible for the Patriots SB wins than their uniforms.
Seattle making the Super Bowl follows the same pattern. Very little history of success, and yes the uniforms change, but don't you think Mike Holmgren has had more of an impact than the Seattle blue color scheme? Perhaps Matt Hasselbeck, Shaun Alexander and Walter Jones are also slightly more important than the color of the uniforms.
If it was all about changing uniforms, shouldn't Arizona have been better this year. Shouldn't Buffalo have made it back to the Super Bowl? Why hasn't Atlanta made it, too? First, when they went to the black helmets, and now again with the recent changes.