Is body appearance more important than weight when dieting?

I started a diet, and I've heard a lot of people say that even if I don't lose much weight, my body shape can still change, so I'm curious.

Looking at the reviews, some people say their clothes fit differently even though their weight remained the same, while others say they are only satisfied if they lose weight as well.

For those of you who actually succeeded in your diet, was weight more important, or were you more satisfied with the changes in your body shape? Please share your experiences! :)