Pros
Job stability (see below in cons), no constant travel, it used to have a nice working environment few years ago. It changed in the last 4~5 years, at least the customer I'm working at right now.
Cons
They will overwork you, regardless which area you work on. About 2 years ago they moved to horizon, which basically killed all promotion options. They call it now "career progression", which means you move horizontally, and in fact, there are talks from HR that your salary may reduce if you go into a position that pays less than your current position. And you will get to know that only AFTER you moved. There is too much pressure with budget, Amdocs has been cutting everywhere they can, every cents counts, sometimes it's unreasonable what we are forced to do.