I think it depends on many factors. Currency exchange rates, VAT, whether you go shopping during the sales season, etc. I live in Switzerland so it pretty much doesn't matter where I go, I will always get better deals everywhere else because everything is overpriced here.
I thought Antwerp had an amazing selection of designer labels and the prices were lower in comparison to, for example, cities in Germany or the UK. Italy and Spain also seem to be on the less expensive side.
That said, I am personally a huge fan of online shopping because it allows me to compare prices and usually I will find everything I want at a much lower price point than what I would pay in store.
Ah well jeans may be cheap in NY (which is surprising given the extra material they use in US sizing ) but a lot of European labels are more expensive, as Kate says they're often cheaper in the country of origin. I was looking at a coat recently and it was $400 cheaper in the UK than in the US.