Pair programming is way faster with screen share & multiplr monitors. One of you has the dominant screen with "the task" and you can both discuss it whilst doing indirect things on your own monitors, and throwing them to the share when they are relevant.

Over the shoulder pairing has a lot of "do this", "search that". Shared has a lot more of "can you work out x whilst I check y" and "this is the result of y, I'm interpreting that as z. Should we do a?".