I don't think I can separate the two. My lifting experience came from playing football and wrestling in high-school, in which power was important. After that though, I've had no need for it other than the fact that I discovered chicks dig guys who can toss them around and literally man handle them.
Always been able to maintain a good muscular frame, but I've struggled with body-fat my entire life. I found though, "fat and strong" is WAY better than just fat. I also found that a bigger chest, back, shoulders makes the appearance of the gut smaller. So then I started pursuing the appearance aspects of it.
In the end, I believe size and strength go together hand in hand, and size helps my appearance, so I value both.