Firecrest have an arrangement with Cabair to allow them to do circuits. Flyteam aren't allowed to do circuits and hence don't do initial PPL training, only rental, checkouts, additional ratings, etc.
The variable circuit pattern is no big deal.
The grumpy controller is indeed grumpy, but he is the only one. Unfortunately he is the one there most often, but again, most students don't find it too big a deal.
Given the number of times a PPL student will be going back and forth to an airfield, the convenience of that airfield is very important in my view. So if Elstree is the most convenient there is no reason not to learn there.