Compared to Garden Warfare 2, Battle for Neighborville is pretty decently balanced because they've completely eliminated the elemental variations of the different character types-- which I'm sure made GW2 absolute hell to balance properly.
It sounds like you're comparing Oak directly to the Imp's Mech in that the Mech has a fuel based timer and the Oak doesn't but that's not the correct comparison.
The Acorn/Oak and the Space Cadet/Space Station are a better comparison--while each has unique attacks both can transform into a larger "tank" based form and both can link with up to three other characters of the same class and neither operates on a timer. If anything the Imp and his Mech don't have an equivalent on the Plant team unless you consider that they are countered pretty effectively by the rooted versions of the Pea Shooter and Sunflower which are both more powerful in that stationary rooted form and can make short work of any Mech.
PvZ games like BfN have always had asymmetrical teams-- both sides either have roughly equivalent character classes or classes which effectively counter each other the way that the Engineer counters the Chomper or the Pea Gatling counters the Mech. It's definitely odd and a bit jarring if you're coming from games like Battlefield or Call of Duty where both sides have access to exactly the same classes, weapons and skills. It's definitely harder to balance but at the same time each unique class has a specific way you should be playing it and not all of the classes will suit everyone.
Back in GW2, when I first started playing, I thought that the zombies had an unfair advantage as well but once I got some experience with each class and figured out the best play style suited for each I stopped believing that and came to understand that there was a sort of quirky balance to the game.
Granted, BfN is new so they'll be fine tuning the actual balance in terms of damage output, accuracy, range and so on now that they have a player base from which to gather data and they've changed some fundamental things from GW2 in some of the classes which crossed over and introduced four new ones so there's a whole new learning process in figuring out how to approach each class all over again and how to counter the abilities of the other side.