I'm not sure how aggressive/strong your Great Tits are, but the chickadees in my yard are pretty timid. Last spring, a pair of chickadees (Perhaps Carolina, but I think we're on the southern edge of the Black-capped hybrid zone) came in the afternoon for several days and put a good amount of moss in our box. Then a pair of Tree Swallows moved in and put a layer of grass on top of the moss. Finally, a pair of Eastern Bluebirds placed a layer of mostly pine needles on top of the grass and moss. It was a three-layer, three-color nest! The bluebirds ended up rearing a (I think, I had to be out of town) successful brood. I don't recall any resistance from the chickadees, but if there was it was minimal.
This year the chickadees checked out the box a bit and were somewhat aggressive with the Tree Swallows, but now we have a swallow nest and no sign of the chickadees at the box.
I have no experience with Pied Flycatchers, but I imagine that they are strong enough to oust the Great Tits. Quite a feat for one bird to accomplish, though, I would expect it had its hands... er, wings... full.