It would be great if people can chose between two systems: the old system with the battle log / journal and the other suggested system where people see the same conversation window. I don't see the issue with different reading speed of the players. You're most likely playing with friends or family anyway, so you can politely ask each other to wait a few secs before klicking on. If you're playing with someone who just clicks through every dialogue, it's fine too because you are equal clueless what's going on at the end, haha.

Please Larian, PLEASE: do something about this. I played D:OS with my girlfriend for 2-3 hours and she was completely turned off by the fact that it was hard to follow each other's conversations. We didn't really feel like playing together... more like playing at the same time, but both on their own. I was very excited about this game and still glad I backed it on Kickstarter, but as someone else already mentioned, this is a real deal breaker.