Oh, dear, you'd be mistaken. Suarez is a magnificent player, easely my favorite player in the entire EPL. But in serie a, thats not enough. Teams would just tactically limit suarez and play negative football against him. Juventus gets this on tevez, but because we have quality in every line, and superior duelling power, we get around that problem.
Liverpool does well in the epl because they cant defend as a team there, and thats exactly what a guy like suarez needs. all that space.
In terms of "big in europe", the EPL hardly has a team in the top5.
Barcelona, Madrid, Bayern, are clearly better then anything from the EPL, whilst PSG has a better balanced team then chelsea, and athletico could challenge any EPL team .