I think the term "big club" is a misused word in these days.
There are many group of clubs:
Biggest clubs: Manchester United and Liverpool
Big clubs: Arsenal, Chelsea
Big-ish clubs: Spurs and Manchester City
Sleeping giants: Everton, Aston Villa, Newcastle
I think Sky Sports has led people to believe that mate. Leeds are a bigger club then Newcastle and Chelsea I my eyes. 10 years can't establish you as a big club. There are 6 big clubs in England to me, Utd, Liverpool, Arsenal, Villa, Everton and Tottenham. Followed by the likes of Leeds and City. Newcastle and Chelsea are still with your Sunderlands, forests, Sheffield Weds, West Hams I think.