I have already said that my using the word "bigger" was probably inaccurate.
But it works two ways. How big a club is can be measured both on its history and overall performance, and also how they were at the time in question. Consider all the Leeds arguments from previously in this thread: Leeds are a big club, but at present they are short of where they should be. As such, even though they are big, at present they don't appear to be "big". The reverse is true of City; at present, they have a bigger stature in the game than they would do if the term "big" is applied to the entire club's heritage.
As such, to use your Chelsea example, they have a bigger stature now than they do as far as heritage goes, and five years ago it was even more blatant. In the 80s, the same applied to Everton, and they probably had a stature within the European game that was second only to Liverpool.
That aside, I don't really wish to argue the case any more. I'm more interested in willing Blackpool to victory.
P.S.: I'm not sure I agree on Roma, but the other nine are definitely true.
EDIT: I have made a couple of edits because I mistakenly I thought Red Star won the '86 competition. It was actually Steaua Bucharest. Sorry!