No, I don't think Julia had agreed to anything, but when someone you love is in an accident, you don't put conditions on saving his life.
As for the original question...I can't come up with a preference at the moment. Barnabas is more interesting when he's bad, so that sort of pushes me towards preferring them to be enemies, but that's not really an applicable consideration. I'm trying to remember a situation in which they were enemies and Barnabas was the good guy and Julia was the bad guy, and the only one I can think of is parallel time, which doesn't count because the Julia was PT Julia, not RT Julia. If RT Julia were the bad guy and Barnabas were the good guy, would I enjoy it as much as the other way around? I suspect I would. Good Julia would never destroy Bad Barnabas because she couldn't bear to, but would Good Barnabas destroy Bad Julia for the good of the Collins family?