For most Europe brands like Louis Vuitton, Chanel, Prada, it is generally cheaper to buy it in Europe compared to other countries in the world. The main reason for that is the VAT Refund you get when you leave the country. Please make sure you leave 6 months from the date of purchase. Generally you will get around 10 – 12% tax refund.
For instance, a designer handbag will cost 1000 Euro in Paris and Rome. In Singapore, it may cost SGD$2000. With VAT claims, one get to save abt 100 Euro and overall, buying the bag in Paris will be 200 Euro cheaper than buying in Singapore, Hong Kong, Bangkok, Kuala Lumpur or any city in Asia.
Most tourists from Asia would buy popular brands such as Louis Vuitton, Chanel, Prada when they are in Paris, Florence, Venice and Rome.
Compared to USA, unless you are looking at USA designer brands such as Coach or Kate Spade, generally European brands will be cheaper in Europe compared to USA.
Another key factor is your currency and exchange rates. If your currency appreciate higher against US dollar compare to Euro, you may get a better deal in USA then.
How much cheaper is it to buy Louis Vuitton in France compared to UK or USA?
Remember prices are only cheaper because of the Tax Refund, so do not forget to do it before you leave the country. You can do the refund at the last stop of any EU nation. Last stop means the last embarkation EU country before leaving foryour home country.