The most obvious difference is that the Archery passive gives you a different bonus depending on your weapon type of choice.
A second difference is the choice for the secondary hand - with a hand crossbow it's either another hand crossbow, a shield or a quiver, while with a bow or crossbow the only option is a quiver.
Finally, there's another very important attribute beyond beyond just the affixes and DPS: attack speed. While DPS dictates how much damage you can do per second, different attack speeds canreally encourage different styles of play. Slower attack weapons can get rid of enemies before they can to you, but higher speed weapons have a mobility and no-overkill advantages. I usually prefer higher-speed weapons even when it means sacrificing some DPS.