Power Levels between Warmachine and Hordes Heavies

Kaya3 wants to activate first to switch fog of war for synergy on the turn she commits (or, in the mirror, to throw up synergy and hide from woldwyrds behind a very large piece of terrain)

Kaya2 wants to activate first on feat turn, otherwise beasts don't get the benefit of her feat. She also generally wants to go first to hotswap forced evolution and/or chuck out dogpile. 

I think I've actually cast soothing song all of once, in years of playing Circle, and that was just to make sure nothing frenzied after running. 

Ahh, you're right. Mixing up my Kayas again...

Kaya1 is hard to evaluate, in that she's a flaming dumpster fire of a warlock. She DOES use it, because her only trick is to yoyo heavies with spirit door (so she usually has beasts running hot and fury to spare, and likes to activate at the end of turn,) but it's not a very good trick, and she's unlikely to see play as she stands. I wouldn't be concerned about Kaya1 breaking the game anytime soon.

It also lets you strip a fury, which threshold doesn't. Though I don't see the need to change threshold at all to get there:

"When a beast succeeds at a threshold check, it has the option to remove one fury"

Would need to be extensively tested, but encouraging frenzy risk is kinda neat. It ought to be part of a broad look at point costs, mat scores, thresholds, new releases, etc as some beasts are doing okay on the power curve as it is.

Another option:
Let beasts run (but not charge) for free. Warjacks needing a boost of energy to get up to that speed makes some sort of sense, which powerup now represents. Animals/sentient beings should be quite capable of running by themselves. They'd still need to land in control range or risk frenzy the next turn. This would also make turn 1/2 when playing into gunlines much easier for a lot of warlocks, who run into a catch-22 where they either have to leave themselves vulnerable, or risk losing critical board position via frenzy or not running a beast. This situation has no analogue in warmachine where casters full camp and powerup-run. As burning transfers still damages the battlegroup (usually dealing more damage), taking those shots is usually worth it even if it doesn't net the assassination. Letting them have a few more transfers that turn prevents frustratingly abrupt endings on the hordes player's side and opens up interesting room for counterplay on the gunline players' end.
It's a little funky that battlegroup warlocks can be earthshatteringly powerful yet struggle to make a group of 8 lights/lessers do the hundred yard dash. Or that 6 "dangerous, unpredictable" maulers can do so just fine but 7 bouncers (whose flavor text is all about loyalty to kin) will break down into a slapfight.

Legion heavies tend to be 9. Nephilim are 10s.
I'm not familiar enough with all of Hordes but that doesn't seem low.

The problem with threshold and fury checks is not that there's a super high chance of failing a check if you leave 1 fury on 1 beast, it's that the downside is terrifically bad. Forget potentially charging your own models, just losing an expensive Heavy's activation is a terrible risk to take, and nothing in WM really compares (particularly when the upside is 'your beast operates at reduced capacity this turn if you pass.' I don't know that marginally decreasing the likelihood of frenzying is going to fix the issue, because as long as there's an appreciable chance, good players won't risk it. The better alternative would be to make frenzy less back-breaking (maybe, beast charges the closest, large based target and makes all of it's initials against it?) so that it's not easily dismissed by the opponent. Right now you can feed a frenzying beast a single trooper, and blunt it's frenzy - if the beast still had the capacity to do damage on a turn it frenzied, it would be a much more reasonable risk to take. 

Remember Mk2 Berserker chassis jacks? Same principle - no one ran them, not because they didn't have the capacity to be decent, but because the risk associated with running them was just too high to justify.

I mean, there's still a risk in that case - the opponent can jam it as if it were a normal heavy, it can still charge your own models, and it's not likely to charge an optimal target (and it wouldn't get any boosts beyond the charge attack.) Nor am I suggesting that's the only solution, I'm just saying that if a true 'risk vs. reward' is the ideal, then the risk can't be as huge as it is. I'd even say you could play with making it random what the beast does - 1-2 it tramples and makes one initial, 3-4 it charges the nearest medium/large based model; 5-6 it charges the nearest small based model, and gains boosted attack rolls on all initials etc.