I'm just past the end of Act One, and my phone is offering the various DLC missions as well as the next story mission. Is there any advantage in holding off on completing them vs rushing to do them as fast as possible? For example, are the DLC missions' rewards likely to make story missions easier, or vice versa? Or maybe the difficulty varies?
Completing the DLC missions, like Lucca Dornelles said, will make the main game story missions easier. Since you can't replay the main game story missions after you finish them (unless you're playing on the PC and have installed a mission replay mod), and you can replay the DLC missions after you finish them, completing the DLC missions as soon as possible may be preferable.
Also, completing the DLC missions are the only ways to add additional 'Brute' homies (aside from Oleg in the main game). So if you want to have 3 brutes with you as homies, completing the DLC missions as soon as possible is preferable. Screenshot of the DLC-added 'Brute' homies (possible spoilers):