Hands down, 15" with a better head. And you are right, it matters what you do, but if you're new, I'm guessing you might want to build a table or a dresser with real wood faces or maybe a nice cabinet or perhaps a night stand? You don't need 20" to do any of that. In fact 12" is sufficient. Why? Well if you don't want that nice table to be as curvy as a mountain road, you better make sure the widest board is around 6" or less. Plane boards to thickness, glue up into panel width you need and cut to dimension. I've build some incredible furniture with a 12" planer.
Bigger is not always better. Bigger can sometimes be just more expensive and not much else. Even if you live and die by the "I'd rather not need it an have it than not have it and need it" sword. Now, if you're a full production shop interested in making money and saving maximum time...buy two 20" planers.