The 70-200 f4L lens is an absolute cracker of a lens. It was my 3rd L lens after a 100 macro and a 100-400 and I replaced my 55-250 with it and the 55-250 went to the wife. It's very sharp throughout the whole range of f stops and the whole focal length, it's quite light and very robust. £300 is a decent price for the lens as well. I paid around £360 for mine and sold it for about the same when I got the f2.8 IS version. If this is your first L lens beware though, your wallet may never be as full again.
The 55-250 is a very well respected lens though, it's got very good optics, the AF speed is pretty good and the IS is very good. If your just replacing the 55-250 for the sake of having an L lens you need to think of what you'd be gaining and losing. You'd gain a great lens with excellent IQ, but you'd lose a bit of reach and IS too. If you're going to be using fast shutter speeds then you wont need the IS though.