Both these anime are actually pretty similar, as both play with the themes of humans and vampires co-existing in each other's worlds. I'd say that when it comes to the MC, the one from Dance is faaaaaar better than the one from Diabolik, who was just dumb as a rock. Anyway, getting to the similarities>
# Female who inadvertently gets caught up in the world of vamps/devils
# MC is a high school student
# Vamps/Devils feel an inexplicable attraction to her, which is later on explained and explored
# Both actually have a plot going on for them, which came as a surprise />
# Despite being reverse harems, both have a way darker feel to them
# Lots of pretty boys fighting over the MC.
# MC's parents are absent from both the anime.
# Both anime have a crazy sadist/masochist with purple hair who stands out from the rest of the cast, design wise.