It's a cliche at this point for people to point out the confusion over who the monster is in Frankenstein. People refer to "a Frankenstein" as what in D&D is called a Flesh Golem - a being constructed from body parts sourced from multiple corpses - but then some will say "no, it's the Doctor who is named Frankenstein." And then, one might say, well, yes, but the Flesh Golem isn't the real monster of that story, it's the callous scientist who created him. And then, my response to all of this, in my most pedantic mode, is that "well, yes, but also the creation can be referred to as Adam Frankenstein, Victor's son, so technically they're both Frankensteins."
All that aside:
Mordenheim's Monster is the stat block designed primarily for Elise, Viktra Mordenheim's lover who died and was resurrected when Mordenheim invented the Unbreakable Heart. Interestingly, it's not clear if Elise actually has that much in the way of other peoples' body parts. Unlike Adam from the original novel (yes, it's more of a metaphorical reference to him being a "new Adam" than an actual given name, but it's what I prefer to use,) who is a wholly new person independent of his source materials (his brain is that of Victor's favorite professor, but at no point does he seem to have any of the professor's memories), Elise seems to mostly be herself.
Now, Elise is also sort of a "model" for other constructs. I believe that Horrors Within also adds another named creation called Adam (bridging, to an extent, the pre-5E lore where it was Viktor Mordenheim and a story much closer to the Shelley novel) who also uses this stat block.
In other words, Mordenheim's Monsters can effectively be considered "elite Flesh Golems."
So, how do they differ?
First off, they're a big step up in CR: CR 12 rather than CR 5. They're also far more intelligent and capable of speech. With a healthy AC of 18, 161 HP, and resistance to bludgeoning, piercing, and slashing damage (recalling the immunity that the 5.0 Golems had) they can actually take a bit of a beating. They're fast, too, with a 40-foot movement speed (and more, which we'll get to).
Basically, this is more like the Jacob Elordi version for Guillermo Del Toro's Frankenstein - smart, fast, and brutally strong (Strength is 22) and capable of carrying on a conversation.
Like their CR 5 predecessors, these are immune to lightning and will actually heal from it when they take lightning damage, but even beyond that, their speed gets super-charged, doubling for a turn if they take any lightning damage.
Indeed, given their neutral alignment (which is also a catch-all for "depends on the individual,") I can actually very easily see a party allying with one of these. Maybe the Sorcerer hits them with a Sorcerous Burst that does Lightning Damage to power them up.
I know it takes a long time for these books to be published, so the design might have been locked before Del Toro's Frankenstein movie came out, but it feels like the overwhelming brutality of the creature in that movie might have inspired the mechanics of this. Even without that lightning-boost, here's what the Mordenheim's Monster can do:
As a bonus action, it can spend 10 feet of movement to jump 40 feet - meaning that it effectively has a speed of 70 - and then creatures it lands on have to make a Dex save or take bludgeoning damage and get knocked prone, as well as shoved 5 feet.
Then, the monster's slam will deal a mix of bludgeoning and lightning (given the immunities and resistances at play, the Monster could theoretically heal itself by just punching itself over and over, but I think that's probably not how I'd have it work). The slam attack also grapples, which is great because the monster can then either crush them or throw them.
Crushing (which I assume is like they're being held up by the neck and strangled) will inflict more damage and cause them to start suffocating. Throwing sends them up to 30 feet, forcing a Dex save for the thrown creature and anyone in their way to take bludgeoning damage and be knocked prone, saving for half.
In other words, this is a monster that will absolutely break up formations. Throwing a target can put them prone and 30 feet away, giving the monster space and time to get to a different target.
I think that a Mordenheim's Monster's turn should feel flashy and panic-inducing. Using its bonus action Violent Leap to get past the higher-AC party members (though with a +10 to hit, they will often be able to hit them as well) and then tossing the Bard or Druid back at the Barbarian or Paladin to knock them all down will make your players go "ok, what the hell just happened?"
The damage output isn't enormous - if they hit twice with Slam and then get failed saves on Crush, that's only like 60 damage, which isn't that much for a CR 12 monster. But they have extreme mobility and battlefield control (on top of their resilience).
Thus, I think that Mordenheim's Monster is best used for hit-and-run tactics. If the party has their hands on a MacGuffin, or perhaps an NPC that they're protecting, one of these could race over to them (maybe sneak up on them, though they'd only have a +3 to Stealth checks,) knock a bunch of people prone with their various attacks, grab what they're looking for, and then race away.
A chase could be fun too - maybe they grab the MacGuffin and are racing along city streets. The party chases them down a narrow alley, only for this figure to suddenly launch 30 feet into the air and continue running along the rooftops.
The Monster is also Medium-sized, and while I'd still be tempted to make them big and bulky, they could potentially be in disguise as just a humanoid.
The nice thing, as well, about having their objective not be the slaughter of the party is that you could pretty safely send one of these against a party that has no business trying to fight one. Any given attack does about 20 damage, so taking even a level 3 character and hitting them with just one Slam attack and then a Throw is probably going to at worst just knock them out, with plenty of time to stabilize or heal them if the party doesn't give chase (which could certainly be a strategic choice on the part of the Monster).
Boy, I really want to do that now.