Short-term, Batherson will be on the team for 2019/20, and should be somewhere in the 13-17 minute per game range. He'll see powerplay time and play mostly on a second or third line. I suspect they'll keep Tkachuk and White together as the de facto top line, so it wouldn't be ideal to have another rookie up there with them. 30-40 points would be a reasonable prediction, but a Calder Trophy run shouldn't surprise anyone either.
Long-term, I see him as a guy who could play on a top line, or carry a second line, but maybe not an elite player. 70-80 points in his prime years would be my best bet.
I really hope Brannstrom plays most of this coming season in the minors. I'd love to see him get some call-ups for the experience, but he needs experience being the guy down in Belleville. He was a top three or four defenseman on his Swedish pro team, and a top two or three guy in Chicago - don't get me wrong, impressive for a teenager - but now at 20, he needs to show he can consistently be an elite player st the AHL level. An ideal year for him would be 30-50 points in 40-60 AHL games, and 15-30 NHL games.
Long-term, Brannstrom's upside is enormous. I could see him as a 23-26 minute defenseman who consistently puts up 50-65 points a year. Like above poster said, could be a Niedermayer-Rafalski (or if I can go way back, Potvin-Persson) situation with him and Chabot.