Although I'm sad to see Branch go, I don't think it's any cause for real worry.
If you had to replace:
1. A large (6-5+ 300+) DT that eats space, holds his ground at the line of scrimmage, and mainly focuses on stuffing the run.
2. An athletic (speed, quickness, nimble feet, explosive) DT that collapses the pocket, pressures the QB, breaks up plays in the backfield, runs sideline to sideline.
It would be much easier to find a player in the draft/FA to replace #1, than it would be to find a player in the draft/FA to replace #2.
Whereas most DTs like #2 would be gone in rounds 1-2, you can still find a lot of DTs like #1 in the later rounds.
Branch was a nice, consistent player, but it won't be too hard to replace him.