zombies going first is a disadvantage because it allows the plants to react with both unit placement and tricks. The attempted balance for this is to allow xombies to react with only tricks against the entire turn of the plants. A good example of when plants are at a huge advantage is when the zombie hero is low hp and doesn't have many units on the board because they have to place the zombies first likely leaving lanes open for plants to place units on that they can't do anything about. As for gravestones, you can get some idea by paying attention to how much brains they spent on it.
I'm not high enough rank to have an opinion on balance but it seems ok to me so far.