I can't speak to the comparison that you ask for, as I don't shop at Louis Vuitton.
Good generic advice is that if you're considering buying something expensive on SBH then it's best if you know in advance what the US price is. You can sometimes do better on SBH, you can sometimes do better in the US.
We have bought LV in the States and in France and in St Barts the prices in St Barts were the same as in In France and it was about 20% less this was about 4 yrs ago