WELL ... comparing cabbage to lettuce is like comparing apples to oranges! Each brings something different to the table.
For example, crowd favorites kimchi and sauerkraut are both cabbage dishes that simply would not work with lettuce. On the other hand, no one wants a floppy leaf of cabbage on their sammich, and cabbage would make a terrible substitute for lettuce in, say, a Caesar salad.
In fact, lettuce and cabbage aren't even in the same family of plant, so though they look familiar, they are very different.
But to answer the question, I think I prefer lettuce. I use it more often, and to me, cabbage seems more of a specialty that you use when making certain dishes, while lettuce seems to be more for everyday sorts of dishes.