We just finished a campaign with me as the OL using the new expansion. I won in the end but it was incredibly close and came down to one roll where if I didn't kill a hero, the rest would have been in range to get to the objective and win. However I definitely benefited from winning the unplayable, broken Heart of the Wild quest so that may have been the slight edge and a few very important rolls ended up as misses for the heroes since prior the heroes were walking through the finale with no difficulty and that swung it immensely. Additionally I had the excellent reinforcement card which just gives monsters that the heroes can't expect and plan around which is a huge power swing in the overlord's favor that other decks just can't compete with. I almost think that card is a requirement. Lastly I realized late how good hell hounds were. With pierce 3-4 they and the nagas with sorcery were the only things that could consistently get through the gray+black+brown dice that all the heroes (including the mages and scouts) were throwing.
I think the problem with balance is related to several issues. Quests are not really well thought out in regards to the incredible amount of hero abilities that can trivialize them. In addition some are just not tested with people that are familiar enough with the game mechanics to exploit rules. For instance in the quest where if heroes step next to spider webs and there is a chance spiders will spawn, as the rules are written you can walk familiars like geomancer stones or the reanimate onto those spaces (since they are not heroes for the effects of quest objectives, only for monster abilities or overlord cards) and the spider will not spawn and then when a hero is adjacent to the now occupied web square the spider has no place to go and the quest doesn't say that it goes to the closest space. Even if they DID spawn the spiders are easy enough to kill it doesn't really matter.
That leads to the next issue in that monsters are too flimsy. The overlord has to hope for hero misses since by the end of an act, most monsters are able to be one shot if the hero is tailored correctly. If the quest has a reinforcement at the end of the turn you can assume that the monsters just won't get attacks at all. The new treasure hunter was consistently putting out over 8 hearts worth of damage with pierce 2-3 so certain monsters just couldn't be taken. The only limit to that is the 1 in 6 chance of missing which makes damage incredibly swingy in attacks that either result in dead or totally untouched monsters. Many monsters also just have no way to break through hero defenses. There are few things that limit heavy armor other than a few that don't allow runes, but still allow magic ranged staffs and none that affect bows. Some have movement penalties but when a character already has a movement of 3 and 5 fatigue and maybe the +1 movement per turn out of action item this doesn't really matter.
Another issue is the skill check system. With the new expansion and access to gear that increases stats along with re-rolls, using cards that require heroes to fail skill checks just can't be counted on. In this game usually there is a situation where one turn makes the difference and having to rely on a 25% chance that something will happen just doesn't cut it. As the game continues the heroes become better at passing tests, but the overlord can't affect those odds outside of a few situations. Additionally it's always better to have the sure thing (cards that buff monsters or spawn them) than ones that require the hero to fail in order for a complicated plan to succeed. One of the ways I think I was able to win was ditching those cards entirely with the exception of dark charm (which didn't work once in the entire game). An additional problem with the skill check system is that most parties contain heroes that have wildly different stats. So a card will typically only be usable on one hero so if that player isn't the one you absolutely need to stop that turn you have a dead card that could have been something better like critical blow, dash or blood rage.
I believe an errata change that needs to be made is that when a hero is down the ONLY way they can interact with the game at all is to be revived using an action. Downing heroes only to have them all stand up when a healer gives them 1 heart with an ability that affects multiple heroes makes the penalty for death meaningless other than a card draw. This is a big deal when in some cases the overlord only gets one monster a turn or none at all.
Certain characters are also just totally busted and ruin games. Silhouette is one such character as several recent threads have noticed. I played as her in a campaign a while ago as a thief type and it totally trivialized certain maps to the point where they made the overlord obviously frustrated with his inability to have any agency in stopping her.
I don't think the overall problems are as simple as one side is overpowered. I think most of the problems stem from the fact that with the Decent 1 ed character and monster compatibility pack there are just way too many variables introduced and no way to adequately test them all. Even without that there are quests that have obvious holes that playing strictly by the rules can seriously exploit.
Overall if I had to make changes to "fix" the game they would be:
1. Remove the extra characters and monster entirely. I think this is huge and probably the easiest thing for players just to house rule. They add just way too many variables in a game where there are so many ways to exploit the rule system. This also removes a lot of the "oh I didn't realize that character/monster did that in this situation" which happens a lot the first time an encounter is played and frankly the first time something is done is probably when the game is most fresh and fun.
2. Make heroes that are down not count as being on the board in any way. The only way they can be revived is if another character uses a revive action on the token that is left on the board in the square they were downed in. This removes a lot of weird exploits and makes character death a penalty.
3. Play test through every quest with each character archetype at least once with people intentionally trying to break every rule possible in order to notice holes. Additionally fix broken quests like Heart of the Wilds.
4. Remove ALL abilities, items, etc that allow characters to increase stats or gain access to rerolls for skill tests. The penalties for these are never really worth the difficulty and in a average group at least one character will have a stat high enough to be able to competently achieve quest objectives so it shouldn't result in heroes unable to complete quests. Heroes SHOULD be failing tests fairly regularly, otherwise why even include a mechanic that by the end of the game is practically ignored. If this requires certain cards to be rebalanced (such as web trap) that is fine.
5. Increase monster health, defense dice or something to allow them to take a hit.
6. Remove certain overlord cards ONLY if monster survivability is fixed (such as reinforce)
7. Monsters and heroes should only have access to massive (2-4) pierce OR additional hearts on weapons and abilities. Sometimes this is hard to stop but I think it's manageable. Pierce should be a way to consistently do a small bit of damage not as a way of adding an extra 2-3 damage points on top of 8-10 hearts worth of health.
8. Make weapons and armor somewhat class specific. For instance mages with heavy armor in addition to damage mitigation abilities makes them better tanks than knights.
9. Take familiars much more strongly into account. They are somewhat outside the game's rules as heroes in some situations and not in others so in many cases they break rules and it's unclear how the quests handle them or make certain quests where having an extra body to clog lanes or sit in certain areas makes the game incredibly lopsided in terms of balance.
A lot of that stuff is way outside the scope of a simple errata but we have players that really like the game but everyone gets frustrated with how often encounters turn into either a blowout in terms of heroes just walking through monsters, the overlord completing a quest without any work because an expansion monster was able to get around a quest's rules, hero abilities not being considered for a quest and making it trivial, etc. A lot of my proposed changes also hit heroes more harshly but as the op noted the overlord has already been tweaked down in several instances in regards to both cards and quest objectives so I think this brings everything more in line.