I just got the option to talk to Ulfric and Tullius about a peace treaty ("Season Unending" quest), and I just want to know if there are any consequences to end the war by joining a side in the civil war instead.
Ultimately, Season Unending doesn't prevent you completing the Civil War sidequest- it just puts it on hold until the main quest is completed. It can, however, skip part of it making the War Hero achievement impossible.
If you want to continue the plot as quickly as possible, do Season Unending. It is far quicker and easier than the war since it is just a conversation. It can also make the war itself easier by forcing the other side to surrender Markarth/Riften.
Neither quest has any unique rewards (everything is levelled equipment) with the exception of the Battle for Whiterun being necessary to become Thane there.