Joe and I tend to replicate the model of a TV writers room. We put the script or outline up on a TV and take turns typing as we work through the Final Draft document. There are definitely teams that divide up scenes and we’ve done that at times, but what seems to work best for us is being in the same room and working together scene by scene. This is probably the least time efficient way to do this but… it’s worked for us.
In terms of arguments – the best idea should win no matter whose it is. Sometimes the best idea isn’t obvious so you do it a few different ways and when you come back to it with fresh eyes the next day/week, you can see which way works best and it doesn’t matter who came up with it because at the end of the day both of your names are on the script/webseries.
Also, Joe and I focus on pitching fixes to problems and not just pointing out problems. This helps keep the process moving along if you’re both constantly working toward making your project better and not just pointing out what doesn’t work.