I've watched few episodes of the original, and they were OK. I love campy, cheesy stuff but it was just to cheesy even for me.
Well, it depends on the season. The first season starts out pretty solid -- family-friendly but not campy or goofy at all (and in black and white, which gives it more atmosphere). It gets somewhat more comedy-oriented as the season progresses, but the show doesn't embrace all-out camp until season 2, a change that was made to compete with Batman (the same thing that drove The Man from UNCLE's embrace of camp in season 3 -- though neither show seemed to understand how to do it right). Season 2 was terrible, and most of the cast was marginalized, with only Dr. Smith, young Will, and the Robot being central. Season 3 tried to play it a bit more straight for a while and feature the ensemble more, but eventually fell back into season-2 habits.