I think that holds true for all sandwiches, hot or cold. It's so easy to make an amazing sandwich just mediocre because of the bread selection. I hate (choosing beggar here, I know) when I go to a cookout and see that the person hosting spent hundreds of dollars on grill food but then went with the cheapest rolls and buns they could find. I almost always offer to bring bread if I'm going to such an event where people are expected to bring stuff. The roll can make or break the plate.
I'm a sucker for onions on my burgers. Sometimes IN my burgers.
I'm the exact opposite. There's just something about getting a CRUNCH when you bite into a burger that makes me cringe....
I'm flexible on that; I will eat them raw, I will saute them in butter and Madera wine, or sometimes even make a tomato/onion jam with balsamic, if I'm feeling fancy.
I go in waves with my burgers; sometimes I like a little pizzazz (I also make what is basically a "marguerita" burger, with mozz, seared tomato, and a basil mayonnaise) sometimes I want straight forward (cheese, lettuce tomato, pickle, onion, mayo, ketchup, salt and pepper).