I have no experience of the City so my opinion and experience is biased. I live in London and love my Bug Bee (though DD is now 3 and walking much more so outgrowing it now). From birth the baby nest was snug and papoose-like and the Bee lies flat so it was perfect for my newborn. Then when she got older we switched it around so the buggy faced away from me and DD could see and engage with the world.
I've found our Bug Bee to be extremely nimble - easily does 360 degree turns in tight spots even when I'm using one hand. Narrow enough to fit through Tube turnstiles, on escalators, small shop aisles. Folds easily. Light enough (^for me^) to carry up and down stairs myself if there's no one around to help me. Extremely sturdy - if I was having another baby then I'd easily be able to get another few years use out of it. Excellent brake.
Oh, and it looks gorgeous! Men in particular seem to like pushing it (male friends and DH) (disclaimer: it's not pink) and admiring it.
We've got a BJCM and have used it from newborn. The backrest didn't swing at all, and the hood is brilliant for sun protection and promoting naps. However, DS did look very tiny in it for a while (and he was 8lb10 at birth, so not a small baby!) We ended up buying a sheepskin liner and a headhugger to keep him comfortable. However, given its price, we didn't resent these additional investments too much