IMHO,not very much.
The briefing is a story,you read dialogues between you,your friend and the squad leader for example.
In game,there are some dialogues,but they are awful:
For example,in third mission (spoiler) you have to shot down a bomber,and you don't have permission to take off and your leader says "what are you doing,you are not allowed " and instead of shouting "WHAT ARE YOU DOING YOU ******** !!!?!?!?!" the tone is like "what....are...you...doing" like all the other default comms.This doesn't help at all for immersion.
I didn't get how the missions work btw,sometimes i come back to base and there is a MIssion -failure also when in game there was the famous il-2 "Mission completed" word in yellow.And also if you die,you can press continue like it was never happened

It's a pity that there is no diary,like pilots MIA,your kill streak,medals or promotions and other things that were in IL-2 default campaign.I really hope in the community work for new campaigns relase,like Mission4today ecc.