Will definitely be interesting to see how relative popularity of the two modes shakes out. For what it's worth many/most of the chapter quests will be BR-only. Meanwhile, Leagues are Dominion-only.
In other words, BR gives you more discrete rewards (especially with the Chapter Pass), and Dominion basically just gives you personal satisfaction and bragging rights. Makes it kinda interesting even as a psychological "extrinsic vs intrinsic motivators" experiment!
[Also, I can't help but mention -- we haven't leaked everything that's coming on the BR side of things yet...]