The whole concept of measuring the "size" of a club is arbitrary, it depends upon how you measure size. Fanbase? Liverpool are far bigger than City. Overall trophy haul? Again, Liverpool far exceed City. Performances over the past decade (i.e. current place in World football)? Well, now you'll find City are actually a bigger club than Liverpool by that measure.
Being a "bigger club" by the measures most use (which is, indeed, fanbase and past success) is all well and good, but it doesn't actually mean all that much when it comes to the present day, to actually winning trophies in the here and now, to attracting top players to join your club. In all of those categories City outweigh Liverpool. Obviously, over time, that can change, but that's not relevant right now. Right now, when you consider the 2015/16 season, and the prospects for future seasons, Manchester City are a bigger club than Liverpool. Let Liverpool have their past glories, as impressive as they are they matter little to the present day, or to the current crop of world class footballers. Winning multiple trophies in the 1970's and 1980's doesn't bring success in 2015/2016. I'll take our situation at present, thanks all the same.