I am a primary plant player and yes, I win most games.

"However, the team I usually roll with has been beaten by well coordinated plant teams on several occasions."

Don't contradict yourself. 

I run solo 100% of the time and depend on randoms. When randoms are doing trash with plants but all the sudden get double digit kills with zombies, it is a clear sign that the zombies have an edge over plants. 

"I only agree with this statement in one situation, concerning electric brain, who is obviously broken. Every zombie has a legitimate plant counter and can be beaten, e.g.: Most zombie skills are cut short with Rose's stun/goatify (including Super Brain's spin attack and Imp's impkata); 3/4 of a sunflower's sun beam bar or pea shooter's gatling amo is enough to kill a mech; Any cactus can 2 or 3 shot a scientist (albeit, with head shots); chomper can swallow anyone as long as they are not in vehicle mode (mech, blot shooter, jackhammer); These are only a few examples of viable counters."

The Rose was only super effective prior patch, after patch they're very easy to handle. Yes, a pea Shooter can take out a zmech by going using it's gatling ability, which makes him an easy target and even then you best hope the Zmech(s) do not see you because you're pretty much dead meat if you plant in the wrong place. The Cactus has slow fire rate and high recoil, the scientist has speed can easily avoid most shots by strafing. Believe me, I wreck cacti with the scientist and I also wreck scientists with the cactus, but the cactus is specialty. Chomper is probably the most useless character of them all. Not only do they become very vulnerable after chomping an enemy, they really don't have any ranged attacks, besides the yeti-chomper and even then it is slow and easy avoidable.

The imbalance happens when you look at the projectile type, damage output, speed, and ammo count. It's really hard to kill a zombie when on top of a building using a pea shooter, unless they're near an object that can do splash damage. Versus being able to shoot plants with pin point accuracy by using almost every single variant there is in the zombie side. The only character that can achieve such accuracy is the cactus and now Citron but Citron is very weak when it comes down to damage output. Let's also not forget most plants show a huge portion of their bodies to be able to shoot and hit a zombie. Where are zombies only need to show their bodies partially, even at times none at all to hit the plants. Which is called head glitching and wall glitching on top of having very low recoil and far distance reach.  

"All but one cactus, sunflower beam or peashooter gatling, many pea shooter variants and all citrons are viable snipers."

Once again, take into account projectile type, recoil, speed, damage, and ammo. The beam and gatling gun make them very vulnerable and I actually find it to be an easy kill when I see planted plants. By the time they realize I'm there, they're basically almost vanquished and those are abilities not their regular attacks. The sun flower can be effective at range, but due to it's damage output it can hardly vanquish much at a distance. 

Conclusion there are zombie variants that do need nerfs, such as: Electro Brainz, Captain Deadbeard variants and the parrot, Imp's Zmech needs another nerf slow speed and may be lower damage output where it forces the mech to choose it's battles wisely and not just mindlessly run into a group of plants and smash everything in it's path. Objective games become impossible to win if there are Zmechs, Allstars, and Super Brainz all over the map.