Ok, so here it goes.

I haven't seen much of Death Note anime and never read the manga. Still, from what I know from L on the series, he looks very different from the one on the manga.
The manga version (from what I've seen in pictures) doesn't look as serious as the other one... He also looks a bit childish and always comes up with that innocent look, touching his lips with a finger.

So are they very differently represented on the anime and manga? What are the differences if so? And does the story also suffer changes?

I think this is it.