I assume that we have currently 3-4 mission servers. Depending on many factors (load, latency) you are connecting to a certain server and receive a number of missions. When you switch instances, if you are connecting to another mission server, you get another set of missions. And so on.
On a "dedicated" server, you will always be connected to the same mission server. That's why you won't receive new missions until they are generated again (15 minutes refresh?).
I don't see any advantages with a "dedicated" mission server, unless the "shared" mission servers were absolutely thrashed by the other server roles on the same machine. Moreover, I hope they will have at least 2 "dedicated" mission servers, for redundancy. Actually, 2 or more will also be best for load balancing, in order to serve quickly thousands of concurrent requests.
I'm sure the architecture is a bit more complicated than we know (they will probably have more front-ends to serve the requests, but a centralized back-end for missions), but unless you were bothered by the constant disconnects (I wasn't for example - I had like one each month), there isn't anything ground breaking here, in terms of player experience.
What would be funny (not the case I hope) is if all missions would be server-side: if one player takes a mission, that mission is lost for the others and disappears from the board.

But I'm sure it won't happen, 'cause everything is generated per session...