Edit: That is to say, I don't think the only value of the demoscene is to create something cool under technical limitations. I think it's to create something cool in a computational medium (the spirit lives on as procedural art, shader art, etc. as well).
Every method of producing a work (done under finite time, I guess :P) will give sometimes vastly different results. Hand drawing an animation will give something completely different under similar time constraints as video editing and completely different from procedural drawing.
To give some examples: you can easily render thousands of points, e.g. stars, make them twinkle, draw thousands of trees, and give them all detailed movement. That's very hard to do by hand. By hand you'll have better control of style, and details like paint texture, etc.. Animating characters (with genuine character) is trivial by hand but quite difficult procedurally (you have to resort to essentially manual animation in the end). There's the question of offline vs online rendering... if you're offline rendering you can go bonkers with millions of objects. I personally like being able to run it real time, I find it gives it a more intimate feeling, and is easier to reproduce (but am not against offline rendering if you find it suitable!).
Also very exciting to me is baking randomness, either with a fixed seed or changing seeds every time. You get a different piece every time you watch it! The possibilities are really vast, and mostly unexplored.