Unless the vanity is in an alcove, I'm not particularly fond of the look of sidesplashes. That being said, sometimes function takes presedence over form. Only you know how sloppy your kids are. :)

If you use a good quality, scrubbable paint, I'd think you should be okay forgoing the sidesplash. Our bathrooms are tiny, and as such, our vanities and sinktops are small. Splashing is inevitable in our situation, and the walls/paint have held up well so far (a few years).