oh_riginal said:

I like how they start off chatting, showing that there is a friendship between them before getting to business, so to speak. The script version feels too much like exactly that: a scripted conversation. The theatrical edit drops in on the mid-conversation which, to me, feels more natural and even makes the actors' performances better.

Couldn't have said it better.

I feel the opposite way about this. I feel that the ANH:R version of it gives the feeling that they aren't incredibly close, and thus have been engaged in simple small talk prior to R2's message. Much better than truly attempting to break into the middle of a conversation.

Obi-Wan was sent to watch over Luke, but was probably waiting for a sign of some sort before he acted (giving Luke a lightsaber, etc.) Without hearing the message, Obi-Wan has no reason to blow his cover and act.

After hearing the message, he has to quickly convince Luke to help him. He does so by telling him a bit about his father, etc, hoping to build some more trust. After all, why would someone watching from afar have a close relationship with the person they're watching?

I definitely hope it stays this way.