Never been to Europe, but I have been to the Biltmore. What an amazing "home" (if you can even imagine living someplace like that - I couldn't!) and gardens. It may not stand up to the chateaus, but it's definitely one of the best we got over here.
You have to understand that this is a huge house, built just over 100 years ago, in the south, without air conditioning. It was a winter home for the Vanderbilts, who spent the summers in New York and Rhode Island.
It's over 175,000 square feet. The family only used it for about 35 years before they started using it as a tourist attraction. I don't know if the Vanderbilts expected to become new royalty, but they had the estates for it, until 1930.
We found the servants' quarters especially interesting. The self-guided tours are routed in such a way that it's hard to imagine living or visiting in the house. But it's very interesting and the sort of thing we should all see at least once.
I went there as a teenager and remember being very impressed. I especially liked their bowling alley and gymnasium - at the time I thought it would be really cool to have those things in one's house.
How much of the mansion is open to the public now? Back then a couple of floors were off-limits, and I remember being very curious about those areas when I visited.
I live in NC, but I've only been to Biltmore once. It's funny, I was just thinking about it tonight before I saw your post. I loved standing out on the balcony overlooking the mountains and wondering if the Vanderbilts ever did the same thing. I was amazed at the servants' quarters and also the swimming pool. I've lived in Europe, but never really went to any of the estates there, so I was pretty impressed with Biltmore. I have no place to compare it to. I really want to go back when it's decorated for Christmas. For those of you who haven't been, it's a beautiful place to go if you get the chance.