I've lived in Sheffield for a year, got friends up in Leeds and been up there a lot. Before moving to Sheffield I had in my head that Leeds was a better place to live, now am very glad to be in Sheffield.
I've taken the train up to Leeds a few times, and on walking out the station I always think 'euwwrk'. Walking up Albion Street it just gets worse. The centre feels cramped, dated and dirty. Stark contrast to what you see as you come out the station in Sheffield, and walk into the centre, up Fargate. (yes 'The Moor' is run down, but only to a similar state to parts of what I've seen of Leeds).
Transport in Leeds seems a joke, trying to get from one side of the city to the other is pain - and all the roads seem to be half dug up. Had great fun getting from the M1 up to Horsforth at the weekend.
Drinking in Leeds seems more expensive (on average) to nights out in Sheffield.
What do you want out of the city? Nightlife? Access to countryside? A big wheel?
Big Wheel is gone from Sheffield now!
Leeds is bigger and better equipped but is out of town, sheffield is a small office in the centre) and have no friends/ family in either location
I think living in the city centre is great, more chance to meet people and go see / do things. If you lived on the outskirts of Leeds, you'd be away from it's centre.. *yawn* or live in the centre and commute out to work.. that'll be fun with Leeds' transport system. If you lived in the centre of Sheffield, you' be where all the people are and could walk to work.