I dont like how people are calling them Good and Evil.
For all we know, both groups can be "evil". or vice versa.
This.
Dawnguard want to wipe out the vampires for obvious reasons; blood-svcking parasites, abominations, predators that feast on the men and women. Dangerous and infectious creatures to society.
Vampires want to survive; to stop the tyranny of the sun to put an end to a prophecy from the Elder Scroll called "The tyranny of the Sun" which predicts an apocalypse for vampires and implies their future annihalition by super-natural means. Wanting to thrive, survive and live on, Harkon wants to stop this.
Both sides have a clear reason to fight.