I do work at Sheffield, but for the helicopter school. I don't know much about Sheffield City Flying School. They seem like nice guys when I say hi to them, and they're pretty busy from the looks of things. The airfield is a great place to fly from, and open and licenced to 8pm which can be useful. A/G radio and very informal, but feels a bit like a real airport...and has nice buildings not an old portacabin, which is nice in winter. On the downside, it's surrounded by areas you're supposed to keep away from due to noise issues, and I don't know where you'd go in the event of EFATO on runway 28. And it feels like an airport, not a flying club, which could be a plus or minus depending on your preferences.
Go along and check it out. If you're there Sunday or possibly Wednesday or Friday, come to Alpha Helicopters and say hi.
If you don't like it there, a student of mine who's a f/w pilot speaks highly of Netherthorpe, just round the corner...very short grass runways and apparently a good flying club atmosphere.