Almost every goalie struggles in a new location/environment.
Yes, the pressure is one thing (and that takes a while to shake) but learning to read the way your defensemen move and the type of shots that will get through is a completely different beast.
Bryz has now had a year to acclimate himself to the Philly system. He's got a year to play with Timonen, Grossman, Coburn, Meszaros. You are right that there is some concern with the new defensemen (they have to replace Meszaros, Carle is gone, Pronger likely not back).
That said, Philly's forwards are going to be excellent defensively. They've got a lot of aggressive forwards and that will limit opposing scoring. Think of where players like Brayden Schenn and Couturier will contribute this year vs. last year. Another year matured will be great.
Personally, I rank Bryzgalov as my 2nd favourite goalie for the coming year (behind Lundqvist & ahead of Rinne AND Quick).
Last year Bryz had a bit of competition in Bobrovsky, but Bob is gone.
He has little back-up competition in Leighton.
Bryz was AMAZING in March last year... which is a good sign.
Sure, he stunk in the playoffs series vs. Pittsburgh & New Jersey - but, guess what, the NHL regular season isn't just against PIT & NJ.
So - I'm not worried.
Timonen-Coburn-Grossman-L.Schenn... that's a very good front four (Coburn, Grossman, and Schenn are monsters size-wise).
With Philly's defensive minded forwards - I think they are prime to be one of the better defensive clubs in the NHL.
My 2 cents.
(FWIW, Bryzgalov was my 2nd pick, #27 overall, in my DobberEntry league draft - so I'm not just chewing it here... I invested in my faith in him.)