No. Barcelona have won loads more than we have. Thats a really poor comparison and there's no relevance to bring us into this.It really doesn't make that much sense though. Are we bigger than Barcelona? They were created 21 years after we were and we had already won the league before them.
Ask anyone who started following more than 120 years ago and they will say Everton...
Chelsea and Arsenal are pretty much on par with each other currently.
Arsenal dominated the league along with Utd for over a decade before Chelsea had won much at all.
They've won loads of trophies, including some over the last decade.
Chelsea are a big club. They just aren't as big a club as Arsenal and haven't won't anywhere near as much besides the Champions League they have that Arsenal doesn't.