Worth noting to the OP that not all Free League games are Year Zero Engine powered. Specifically Twilight 2000 is its own thing
First statement is true - Dragonbane and Symbaroum do have their own engine (d20 roll under), as has The One Ring. The second statement, however, is IMO only kind of true. It's correct that T2K has its own system which (mainly) uses two dice which go from d6 to d12, however, Free League has decided to also call this Year Zero engine. So now there is Year Zero - Pool Version (directly derived from Mutant Year Zero) and Year Zero - Step Dice Version (derived from the T2K system). While I found this a bit odd in the beginning, except for the dice types, they are similar enough that I can see why Free League decided to do this. Besides T2K, the Blade Runner game also uses step dice. I like both, but I think they fit some genres better than others - personally I think that the pool version fits survival-oriented scenarios better and step dice work or would work better for games with a different focus (e.g. I think step dice are a good fit for Bladerunner and I feel Tales from the Loop might work better with step dice).
Generally, Year Zero games have the right amount of crunch for me, though T2K is a bit above my preferences. My personal favourites are Forbidden Lands and Alien (the Evolved Edition even a bit more than the original); Vaesen and Tales from the Loop are fine, though I'd prefer characters to be a bit more competent (which is something that a few players strongly dislike) and I feel both would be better served with step dice (though Vaesen would require more tweaking for this). I have yet to play Bladerunner, so no final verdict on this one (reading impression is good, though).
The trickiest one is Coriolis. First, Coriolis The Third Horizon has a great setting, but a terrible (IMO) campaign, and the game system also feels like the least polished version of Year Zero to me. There's also the new/upcoming Coriolis The Great Dark, but that's less of a second edition and more of a new game in the new universe.