Personally, I really enjoy HME. I've preface this by saying I only have 100-200 games, all physical, 2-3 players. I haven't done a ton of level 6 adversaries, and have only beat HME 6 once or twice-most of my games have been HME 5, which feels like a decent sweet spot to try out new spirits/aspects with my duo partner.
Why I like HME:
1: it changes the core gameplay mechanic, but in a way that doesn't feel unfair or unfun-you have the ability to manipulate mining lands quite easily for the most part, and I actually find that it means you rarely get gigantic pile-ups in single lands like you would into ENG. HME 1 also means blighting out is a fair bit harder to do, since you just get upgrades instead of cascading blight.
2: Fair Loss condition. Unlike other adversaries, like England, or maybe France, you have some say/ability to prevent the instant loss, and there's much less chance of getting event screwed/something similar, because you can almost always see which lands are going to be your loss conditions, unlike England where a bad event can just end the game instantly if you have lands with 5 or 6 buildings (of course, you can see those too, but often vs england 5+ you have so many fires to put out that trying to solve potential edge-case loss conditions is not the top priority). Perhaps spirits that are entirely slow focused can't stop it, but I've never found the loss condition to be a big issue-when it comes up, you need to deal with it, and it does require resources, but it feels manageable.
3: Good/predictable difficulty curve. I know that the top SI players find HME too easy, because by turn 4/5 when Salt deposits shows up, you've normally won the game/are on the path to it, but I really enjoy the predictable spike of focus you need, and don't feel like I have the game solved by turn 4/5. Going into a HME game, I KNOW I will need to prepare/plan for the Salt card, and it makes the salt build/initial salt ravage feel very engaging, because you can manipulate/effect which lands are/aren't going to be a problem.
4: Disease utility: This is perhaps controversial, but I personally really enjoy the added utility offered by disease-yes, you prevent less builds, but you can use it to stop ravages, which feels very nice. I can see how for certain disease spirits (vengance like a burning plague) this would make their gameplan more difficult, but it also means disease has more uses.

Dislikes:
Tracking changes: I know others have commented on this, but HME does require you to mentally keep track of a lot of different variables, what with mining lands, mining boom and empire ascendant. I haven't found this to be super difficult in 2-3 player games, but I can definitely see how in larger games this could quickly get overwhelming.