It seemed like we were always
off on some trip or other
involved in some escapade or other
(note the evaluation here is also set back in the past, 'seemed')
is the usual way of showing the mindset of foregrounding prominent memories (so that regular events are promoted hyperbolically to durative consideration).
Only the ...
The difference is one of frequency, intensity or emphasis. "used to do" implies a lower degree of at least those one of things than "were always doing".
For example we could say "We used to go to Brighton for our holidays every year" or "We were always going to Brighton" but the first of these implies that you went ...