It depends on what you purchase. Often brand name products such as Longchamp, GEOX, etc can be found cheaper in the US (unless on final sale prices in Europe) Other products vary; I just bought a pair of Papillio Madrid for €24,90 with free shipping vs the $70+++ I have seen in the US. If one knows where to look for sales at which time of year one can generally find the 'best' price, whether in the US or in Europe.

My Sephora makeup is a little cheaper still in the US.

For the most part, drug store prices are still much cheaper in Europe/UK. For instance, full size 3-1-1 compliant toothpase is around 0,55 (for 75ml or 100ml); Boots products are often on sale for 3-for-2 or £1. Even with the exchange rate, those prices are better than what I see in the US for decent quality items. (Of course, there are not generally coupons in Europe for those crazy 'free' shopping trips at CVS etc) I'll happily spend time at Monoprix, or Rossmann, or Boots, comparing prices on the better quality toiletries and beauty items, and buying whatever is a decent price whereever I am at the moment.

My standard 'stock up' list includes for instance £1 Boots Ingedients shampoo, conditioner, bodywash, and £1 Boots house brand tampons when I am in the UK (or in a country with a Boots with similar prices, such as Thailand or the Channel Islands)