I think part of why Zombies seem overpowered at first is that their decks are bottom heavy, that is to say that their basic and uncommon cards are cheap with good abilities (deadly, gravestones, bounce plants, bonus attack) but their legendaries are all high cost cards (trickster, zomboss, gargantuar feast) but the plants their basic and uncommon cards are nothing special but they have some really good cheap SR+legendarys so while you may find it hard to keep up with the basic cards you start out with, it gets easier as you start to collect SR and legendarys but when for the zombies it gets harder because the plants start to have good cheap cards.