The main reason for why playing zombies is easier right now is because starting players first have access to plants, so they play more plants, so a zombie player is likely to be matched against a lower rank plan player who has fewer cards and knows the game less well. The opposite happens with plants. Due to the long wait times, high ranked players are only playing with zombies and thus it is more likely that a plant player will be matched against a higher ranked player.
As far as balancing, I promise you that it might feel unbalanced, but once you get to know the cards and tricks better you'll see that actually it is quite well balanced. Playing creatures second gives plants a very big advantage over zombies and playing tricks first allows plants to buff their own plants and kill zombies before you can buff them or do bonus attacks to finish the game. Once you start getting matches against higher ranked plant players, you'll see just how potent they are, or you may find that yourself as you gain experience.
You should probably know that most veterans consider plants to be the slightly more powerful faction due to some rather nasty tricks they have at the higher rarities, but even just with commons and uncommons they are pretty much on par.
Also, here are a few counters:
Arm Wrestler -> any direct damage or debuf. or Bonk Choy at 1 sun. You can also Combo something like Snowdrop and Iceberg Lettuce. Don't worry if they play it first turn and you don't have an imediate counter, they eventually come up. Another good counter is actually Pea Pod. If they played the wrestler turn 1, you can play your Pea Pod and your's will automatically grow, no questions asked. then they have to deal with it but you can buff it, move it or block it and they are in trouble.
Tennis ZOmbie, ignore its first attack, then just leave it there to fill up your block meter.
Gravestones ->Gravebuster obviously, and if you don't have it then you need to know what it might be (this takes some experience) but its just a question of playing in front of, or not.
Chicken Mascot imp is a risk for the zombie player. If they play it at 3 brains, they run the risk of it bein taken down by something like Shrowm for two plus BUff-shroom (a deadly combo that counters a lot of things) or simply a Zapricot.
While its true that certain matchups are harder, it goes both ways.