Canon 70-200 F4 is a great lens, I still own one which my son uses. Constant F4, light, great performance,
BUT
The EFS 55-250 is quite a rated lens, for the money and fts in nicely with the kit lens of 18-55. I'm not sure a lens in the 70-200, 70-300 lens would give you more, especially swapping a f4-f5.6 lens for another.
What other lenses have you got at the moment, what camera body and what issues do you have at the moment that makes you think the 55-250 doesn't work for you? What sort of things do you shoot? Perhaps theres another suggestion?