For the 380 in economy, I try to see where it is likely to have an empty seat next to me. If the plane (rarely) is not too full, I try to get a seat on the upper deck Y in one of the 2-seat side areas. It is correct that the overhead bin is much narrower, but to the left of the arm rest there is room for small handbags.

If the plane is completely packed, I will choose the lower deck close to the front as the time it takes to unload so many passengers becomes tedious after a 10 hour flight.

To the US, interestingly, my last trip a couple of weeks ago was the first time that I encountered not full flights (into ORD, back from JFK). So I would pick an aisle seat (my preference) in an economy row where the window seat was already taken. On both legs, the middle seat in between was empty for the flight. Not sure if this is a sign of tourism dropping to the US which I've been hearing about, but have seen no data.