I think even in his last three seasons with Chelsea, he wasn't at the same level he was when he was the best keeper in the world in the mid 00's. I don't think under a new manager things will change too much imo. My personal opinion on it is Cech is just happy to be In London as his family is settled there and a bonus is Arsenal came in for him, not a major step down from Chelsea sure he won't win titles but he get CL football, might win a cup here or there, play week in and week out, get paid nicely. But I don't think we ever see the best of Cech cause I don't think he has it in him anymore, unlike Buffon who gets better with age Cech seems to be the rare case of getting older doesn't mean he get better. I think he's still a solid PL keeper and will do a job but I think we can get better, Cech will be a good back up but I doubt he want that.
It was a good move for the club to make but sadly I don't think we got the World Class keeper we needed.