Their effect is quite different, 2deathy.
Whenever D.D. Warrior attacks or is attacked, no matter what the result of the battle is, he will remove himself from play along with the opposing monster. You can attack a defense position monster and both monsters will be removed.
D.D. Assailant must be destroyed by battle in order to gain his effect.
Additionally, D.D. Warrior is DARK and with <1500 ATK he's searchable by Mystic Tomato and Sangan and is also Allure fodder. D.D. Assailant is not searchable.
Now, all this being said, the card run most often is D.D. Warrior Lady, who takes the best of both worlds and adds better things. She has 1500 ATK so she's searchable by Sangan and Shining Angel. She is LIGHT so she can be used with Honest. And last and most importantly, her effect is OPTIONAL, so it isn't mandatory to remove her from play at the end of a battle, but you can choose whether you want to or not.