I am trying to decide whether to get 215/45/17 or 215/40/17 on stock s lites on a cooper. I haven't lowered it yet but was just wondering if there was a big difference in size or rubbing anywhere or are the 40/17's to wide for the rims?

 

The stock S-lytes are 17x7" and if you don't lower the MCS then you will have plenty of room for now with either of these two tire sizes.

The problem arrises as you lower the MINI the set of springs you choose could result in some rubbing if the tire shoulder is rather broad and square as is the case with H-sport springs and Yokohama ES100 215/45-17 tires which I have and they rub in the rear wheel wells with aftermarket 17x7" rims with 42mm offset.

The 215/40-17 would decrease the chance for any rubbing even with lowering springs added but the tire load rating for that size is below the load rating for the stock sized 205/45-17 tires. So don't put too many people and their luggage in a MINI if you have those 40 series tires. Neither tire is too wide for the stock rims.