Vector graphics produce high-quality animation at all resolutions, with very small file sizes.
Flash was used to create almost all such animation you see on the Web today. Tiny, simple and non-interactive animation can often be implemented as animated GIFs, which are not Flash's specialty, and for which Flash is usually overkill. As the animation get more sophisticated and interactive, however, Flash proves its worth. None of this discussion, however, should overshadow the fact that LiveMotion is 1.0 software and is therefore the new puppy on the block, while Flash is a seasoned, full-grown pit bull.