I agree with much of what you say. I don't know about plants being "OP" (depends on your definition I guess) but they are strongly favored over zombies right now. Over on the PvZ Heroes subreddit, there's a lot of talk about how plants seem to be generally more powerful than zombies at the moment. Specifically, there's a lot of hate towards clique peas.
For what it's worth, I also find it much easier to rank up as plants, both due to the matchmaking often giving me games against lower ranked opponents, and also the quality (cost, stats, abilities) of the cards I'm able to play.
That being said, I like the challenge of playing the zombie side sometimes, so after reaching a new rank, I'll switch it up and play Huge Giganticus / Bad Moon Rising for a little while. It doesn't win as consistently, but when it does, it absolutely destroys heal decks, clique peas, flower decks, and whatever other garbage the opponent tries to throw at me. Occasionally it'll give you something bad... it's RNG after all... but more often than not, I win either that same turn or the following one. I also once pulled off a turn 3 Plankwalker with HG, and there was absolutely nothing the opponent could've done to prevent it!
I think in general, as a zombie player you have more to "think about" during the game. It goes without saying that the plants are able to play more reactively, given the turn order. As a zombie player, you have to think... what plants can they play this turn, and how can I prevent them from being a problem? Are they likely to have certain cards in their deck based on what I've seen so far? If I play a certain card, are they likely going to have a good answer to deal with it? How many brains should I save for the trick/environment phase? Am I doing enough to keep the opponent guessing? Can I force them to stray from their strategy to deal with mine? As a plant player, all you have to do is look at what the zombie player did initially, look at how many brains they have left for tricks, and play accordingly. Predicting gravestones is another skill you need, but it gets much easier with experience... and at the higher levels you might as well assume the opponent already knows what it is.
In the end I've decided that if I feel like winning easily and ranking up, I'll just play as plants. Once I'm bored of that and I need a challenge, I'm playing as zombies!