Ralph Lauren - In store or online?

Same price between online and stores. I believe the stores (the two in DC area at least) carry nicer items than the website. More black label and purple label suits, ties, shirts, coats. In house made to measure. You can also try on the items of course. Great service too as they usually offer a beverage if you'll be there a while.

Can't speak to stores/online in Europe unfortunately.

I think outlets are cheapest.

European stores have an extra fit, which American stores or webshops don't have, and that's the "slim fit" which is more fit than "custom fit".

I've begun seeing "slim fit" polos online. Never checked for stores.

Outlets are the cheapest but I can only find purple labels there. Although the prices are the same I would recommend checking the stores, they generally have nicer suits and shirts and not stalker-ish service.

It's nice to see how you look in the products too I guess 

Like most US-brands, RL is more expensive in Europe, just like European brands are more expensive in the US.

It depends on the outlet. I have visited many outlets in the US where they don't carry any Purple or Black label items. I have been to a few outlets in Europe - one had a few PL and BL items and the other didn't.