Zombies Are Stronger Than Plants

I disagree with you. It is pretty hard for a zombie to burst a plant heroe, while the plants can do it pretty easily.

(Re-Peat Moss + tricks, Heartichoke+Flytrap, Magnifying Grass + bonus attacks, etc.)

As a Zombie main I think that zombie heroes require MORE strategy than Plants, just for the simple reason that they have 2 phases in which the resources are shared.

You need to think in advance to save some brains for the trick phase.

(Unless, of course, you are just playing buff cards like the Going Viral).

But in the end, this is just my opinion.

zombies are generally easier in my opinion. This is because I think Zombies are much much better equipped for playing dedicated decks. Especially because the Turn-Order of Zombies, Plants, Tricks can be easily played around by most zombie decks. You either have Gravestones, Summoning tricks (or teleport which technically exists twice now) or both. Plants on the other Hand can not really break out of their set of rules of that single phase and rely A LOT on the combat phase.
Extra attacks for Zombies are much cheaper and more numerous which also emphasizes the zombies ability to break out of the set turn order. 
To be fair it is kind of balanced around this. You can see this at how hard Zombie players struggle to hold the upper hand when the Plants do their thing pre-combat. ( see moss as a prime example, although there is decent counterplay with mixtape bucket and backline defense).

That said; you can see at how much better the average of zombie cards are at how broad their options are to build decks. Zombies have various good midrange decks. Such as Neptuna Gravestones for example; Zombies have a decent amount of hard control decks; classic valkprof is a good example although a bit out of fashion; Zombies can also play aggro. All zombies lack is OTK Combo. and seriously? Trickster is pretty damn close to otk at the point where you play him. I mean its not unusual that you get smacked with two of them as a finisher.

So what decktypes do plants have? As far as I know there are not Tier 1 midrange decks. MAYBE Zilla and knuckles but....no not really. Plants sure do have good control on a few heros, yes. still worse at raw control than zombies.

Plants  can play aggro in some way thats en par with zombie aggro I think. and guess what: Plants can play combo.

All you have to do is to play a deck thats good against combo and aggro and you are very likely to have a good matchup. Plants have in general much more to consider.
To be fair; Zombies as Plants both have weaker and stronger classes. I just feel like Plants got pushed into a wierd corner where you either play proactive and loose or you play combo, while zombies got good hate going and their new good cards are evenly distributed among their classes....while for plants....MORE COMBO!