I use Delsey bags (on case # 3 in 15 years, last time I upgraded was to get a smaller bag in line with European carry on rules, not because I didn't like bag
#2 ), both for the wheeled bag, and the bag that slides over the handle, and I don't experience snag - I agree with the poster who said it is more about the width of the sleeve part on the second bag, than the handle of the first.