Trevor Booker could never shoot, wasn't a particularly good finisher at the rim, had very limited ability to handle, and was mostly a straight-line driver. He was the epitome of a backup energy big who would play defense, crash the offensive glass, and bring emotional energy and toughness, but that was about it. His lack of shooting and finishing made him unplayable and pushed him out of the league.
Brantley has the ability to play and create out on the perimeter. He's got some handle, hesitations and crosses, the ability to backdown, and a variety of ways to finish at the rim. He bullies smaller defenders, and he uses his length to score around bigger defenders. He can shoot off the dribble, both from distance and mid-range, and he's even developed a pretty good floater from 8-10 feet. The thing that's most surprising is his ability to fire passes off the dribble with timing and vision.
If you want to compare him to someone, compare him to guys like Paul Millsap, Royce White, Boris Diaw, and even a bit of Paul Pierce. The way he'll earn his way onto the floor is by playing hard on defense and crashing the glass, but he's got a lot of versatility and ways to contribute in Quin's system. If Georges Niang wasn't hitting 43% of his 3s right now, I think Brantley would already be getting some rotation minutes.