I have been reading on the web about a sort of "match" between backpackers and "luxury" travellers. First of all, I'm not sure why who doesn't travel with a backpack is seen as a luxury-traveller. I never "luxury-travel" and I never backpack, I just travel.
I think the main difference between the two "travel-types" is meant to be the amount of money someone is able/willing to spend when travelling. One of the main aspects, apart from the type of luggage, is the diference of the places travellers choose to sleep: backpackers usually prefer hostels, other travellers stay at hotels.
These two differences aside, I don't think there's any other reason for argument.
As for myself, I'm usually quite close to a broke status, so I always travel on the cheapest budget possible, however, even if I'm aware that hostels are much cheaper than hotels and B&Bs, I can't think of staying at a eight-bed dorm (I know, I'm not twenty anymore).
Also, I'm not able to backpack. Literally. First of all, most backpacks are bigger than I am; second, I don't know how to stick all my stuff in it without messing it and crumpling my clothes.
Besides, if men have invented the wheel, why do I have to carry all my stuff on my shoulders and cause myself a sure backache, when I can easily use a trolley?
Yes, I confess, I use trolleys. They are small, easy to handle, they fit comfortably in the proper space on the buses and my clothes don't come out crumpled.
In fact, another myth is that only backpackers use the public transport. When I arrived in Ireland, my choice was between the Dublin car rental and the 16A: I didn't wait for the bus only because of money issues but also because, coming from Italy, I would have surely tended to drive on the wrong side. But this is material for another post.
My tiny black trolley? It's used to buses and any kind of adventures.