Being at an American show looks like visiting a cinema or the opera.
There's hardly any dancing or jumping around, lots of people milling around buying snacks and most importantly poor crowd interaction. You can hardly hear the crowd singing, this was very evident on the MSG previews.
Also and maybe the biggest factor, the European crowds are way younger and consist of more or less a 50/50 male to female ratio. American crowds are older and more womanier (Not a word I know

)
There's nothing wrong with either experience, just one feels better in my opinion.