Yes, Intellivision BurgerTime was the best. It was always just too clunky on other systems. I never put it on the controller, but there is probably something to that.
As to the main question of this thread, I don't really recall what it felt like to have an Intellivision. . .I was probably only about 9 by the time our family system died. But I do remember getting up really early to be able to play it before the older siblings got to it.
I struggled with some more complex games like B-17 Bomber and Bomb Squad, mostly because I was so young. But I remember playing games like Buzz Bombers, BurgerTime, Bump N Jump, Maze-A-Tron, Masters of the Universe, Skiing. . .more than I do playing Nintendo games.
Unrelated, but something that is on my wish list for the new system (not to go off topic too much here), but Horse Racing was a popular game, and still is:
I never had the Horse Racing game, but I had a friend that owned a bar that was also an arcade, and they had a giant screen game with a huge brass rail where multiple players could sit. You created and trained a horse by first choosing its parentage and it was stored on a removable card that you could keep and plug in later at any time to continue its career. I haven't seen horse-racing as a listed or suggested game/title as of yet, but would love something similar with an 8-player option.