The main conflict between the two is that juror Number 8 did his homework and juror Number 3 is basing his verdict on the fact that he doesn't give any slack to those from the lower class because he simply doesn't like them. But one of 3's biggest problems is that he wants the deliberation over.
Example:
Juror #8 says that the boys would never yell, "I'm going to kill you."
Juror #3 later attacks #8 because he's irritated he's keeping them there. Juror #3 yells in anger, "Let me go, I'll kill him, I'll kill him!." (at #8) To which, #8 says soemthing like "you really didn't mean that, did you?"