Start start start.
Start.
The hardest and most technically important lifts need to go first. Why? Because they are hard and technical, you need to be fresh for that.
The risk of injury with deadlifting is greater due to the multi-joint total body nature of the lift, plus the fact that the deadlift usually involves a lot of weight compared to other lifts. As a society that that sits way too much, we are making ourselves predisposed to discogenic patholoy (weakened discs available to bulges or ruptures). A great way to exploit that disc injury susceptibility is to deadlift with poor form.
Even if you don't get hurt with iffy form, you really want to be hammering proper deadlift form. You need fresh muscles to do that. If you deadlift with iffy form consisently, you are developing faulty motor patterns that may eventually lead to injury once you use heavier weight.
Start with the deadlift.
The deadlift is such a beneficial lift for strength. If your goal is strength, you really need to be doing them first. If you feel you can still pull the same after training other back exercises, you aren't deadlifting well and/or you aren't really pushing yourself to pull maximal weights. The lats play a huge roll in the deadlift. Rowing or chin upping before hand is going to effect your pull.
I wouldn't even do deadlifts on a back day in the first place, as it is in a most functional sense a lower body lift. Of course it is really a total body lift, but it is significantly more lower than upper. In terms of how training days are split up, it is going to belong on a lower day most of the time.
I never get the whole deadlift for an upper body day. The upper body muscles are working, for the most part, isometrically. The concentric and eccetric actions are invovled in lower body/hip musculature. The acceleration and decelleration is coming from there. The glutes and hamstrings are the prime movers. It is simple kinesiology.
