I would agree with Drakulie. It will be different but that does not make it better. There will be greater initial tension loss if you pull once rather than twice. That is only a problem if you don't like the lower tension.
Let's say the OP experiments with the same string at different tensions for several months. If he always pulls once, he will arrive at a tension that works perfectly for him. If he always pulled twice, he would still arrive at the same actual tension that works perfectly for him. The difference is that he will be using a higher setting on the single pull machine to compensate for the greater initial tension loss.
In the end, it is exactly as Drakulie said - double pulling is not better just different.