Zyra main here with over 200K points.
I can tell you the difference between Brand and Zyra almost immediately upon playing the former.
Brand's W takes longer to complete than Zyra's Q, and is therefore more easily sidestepped in the early game.
Brand severely lacks any kind of hard kite; whereas if I build a crystal scepter on Zyra, the autoattacks from my ranged plants apply a 20% slow (which oh by the way, stacks and goes from 20% to 40% if two plants are dpsing the same champion). You can also used the slow mechanic to stop champions from fleeing. If someone is over a ledge (like at dragon) and your teammates can hop over, but you can't, throw a plant or two on the other side and watch as their autoattacks prevent the fleeing champ from gaining the distance needed to get away.
Also, the sustained dps from having plants up applying the Liandry's Torment dot during teamfights is amazing.
Brand is pure dps. He is easily caught out and bursted down/cc'd, and doesn't have any reliable way of avoiding this. It's true, his kit will out dps Zyra's by a small margin in the right hands, but is it really worth losing an AOE knockup/disruption, a snare that can hit multiple champions, and a 40% slow that you can use to dance around any melee that comes after you or other squishies on your team?