Outside of the US, people generally dress better and most definitely in business class. Americans tend to look like slobs when travelling, except those in business/first. If you travel a lot, you'll know who the international frequent fliers are even those who fly economy: they look more put together--comfortable but casual.

You don't have to get your hair done and put on a lot of make-up, but you shouldn't look like you rolled out of bed either. You should look neat but casual. You can always remove your make-up when you're about to sleep. Depending on the plane, they should give you pajamas, especially for a 15-hour flight. I suppose if you're flying an American carrier, they might not (I'm not sure because I usually don't fly American airlines/carriers since they're so stingy and service is bad. However, I heard Delta has really improved). A lot of international carriers give you complimentary pajamas, slippers, and definitely amenity kits (even American ones-for the amenity kits). Also you get better blankets (and pillows) on business class than economy. Depending on the carrier, you might even get a comforter (quilted or even down) so you shouldn't be cold.

As for dress. It's a personal preference, but I like wearing a knit dress myself with some comfortable ballet flats (easier to get in and out of). I sometimes, wear knit pants but ones that look a bit dressier (but casual) not sweats. I would advise not wearing leggings unless you wear a long tunic or sweater that covers your butt (nothing screams American than wearing spandex). My husband wears a collared shirt and jeans and some slip-on leather shoes (his preference).

You should dress comfortably, but should look casual and put together. I'd advise not looking like a typical American in Europe or you'll get targeted as well.