I've never run a Kraken fight, so this is all going to be theoretical. But unlike the Lich, whose MM design really focuses on spellcasting as its primary turn-by-turn action, the Kraken uses more straightforward attacks and beefiness to challenge the party.
Flee, Mortals! gives us its own Kraken, and it's one of the highest-CR monsters in the book, falling only behind Goxomoc and Xogomoc, which are the two phases to its Tarrasque-equivalent. The Kraken is a rare "villain" solo monster that isn't meant to represent a specific individual monster, but much like the Monster Manual's version, this is not just any sea monster, but a Titan from an elder age.
So, before we look at MCDM's take on this creature, let's remind ourselves of the WotC version.
The Kraken is a CR 23 Monstrosity with the special "Titan" subtype that I believe is only shared by a handful of other creatures, such as the Tarrasque, the Empyrean, and I think the Astral Dreadnought. Titans are, in D&D terminology, either the lowest tier of deity or the highest tier of non-divine being, often having some close connection to the gods. They're meant to be a big deal, though I'm unaware of any magic item or spell or whatnot that actually cares if a thing is a Titan.
The MM version has 472 HP, an AC of 18, a walking speed of 20 feet and a swim speed of 60 ft. It has proficiency in every saving throw other than Charisma, immunity to lightning and nonmagical weapon damage, truesight to 120 feet, and immunity to being frightened or paralyzed. Shockingly, it does not actually have Legendary Resistance, but it does have Freedom of Movement, the Ambiphious trait, and the Siege Monster trait.
Its multiattack lets it do three Tentacle attacks, which have an attack bonus of +17 and deals 20 damage and grapples the target, and they can replace any of these with Fling, which lets them throw a grappled creature.
It can also Bite, which has the usual swallow effect that deals 42 damage per round. Finally, it can do a Lightning Storm that can hit up to three targets for around 22 damage on a failed dexterity save, or half as much on a success.
Then, we've got three legendary actions - Tentacle or Fling costs 1, Lightning Storms costs 2, and for 3, they can do an Ink Cloud, which heavily obscures an area and deals poison damage.
So, honestly, the Kraken's not too complicated to run - it basically hits pretty hard, but probably needs to swallow player characters to really cause any serious panic. It's fast in the water, and thanks to Freedom of Movement, it benefits a lot from using difficult terrain, while its ink cloud is good coupled with its Truesight.
Still, the Kraken's main dangers are pretty mundane - it hits easily, hits hard, and can restrain you. The numbers are big - it's a ton of hit points to get through, and while the damage isn't shockingly high for a likely tier 4 monster, the fact that it has a +17 to hit means that it's going to be very hard to not get hit by it - someone wearing mundane plate is only getting missed on a natural 1.
FM's Kraken is a higher CR - it's CR 26. There's also a rider on it that makes the Kraken effectively immortal - when it drops to 0 HP or dies, all conditions end for it and it teleports back to the place where it slumbers, where it regains all its hit points and falls unconscious. In other words - the Kraken is an eternal part of the world, and can only be repelled, never fully gotten rid of. But I'd also probably say that when it goes unconscious, that's probably something that will last for thousands of years.
This Kraken has Amphibious and Siege Monster, but it also has Supernatural Resistance, as well as Slowed Resistance - a version of Legendary Resistance that, three times a day, lets the Kraken turn failed saves into successes but incurs a 10-ft movement speed penalty that lasts for 24 hours.
This Kraken has an AC of 22, 499 HP, and a land speed of 30 feet with a swim speed of 60. So, if land-bound, using all its Slowed Resistance will lock it in place. It also does not have Freedom of Movement. This Kraken has cold and psychic damage immunity in addition to lightning and mundane weapons. It's also immune to more conditions: blinded, charmed, dazed (a special condition in MCDM stuff,) flanked (which MCDM treats as a condition), frightened, poisoned, paralyzed, petrified, or stunned. Its Truesight isn't quite as long-range at 60 feet, but it has blindsight out to 120 feet.
The Kraken's Multiattack allows it to use its Tentacle attack four times, or it uses its Mental Lance attack three times. Interestingly, it cannot mix and match here. The former is, of course, a melee attack, while the latter is a ranged "Power" attack (MCDM's stuff distinguishes psionic powers from spellcasting beyond simply not needing components - it's a wholly separate thing).
The Tentacle Attack has a slightly lower hit bonus - a mere +16 - but deals a lot more damage: 19 bludgeoning and 11 psychic. Like the MM version, it grapples targets, but unlike it, it does not restrain them. Mental Lance has a 120-foot range and a +18 to hit, dealing 22 psychic damage and frightening the target. In a certain sense, this kind of takes the place of Lightning Storm, reimagined as a psionic thing that does psychic damage (not as good for my Blue Dragonborn EK, but better for my GOO Warlock).
They have an action called Psionic Storm that allows them to restrain a vehicle, and destroy it if they keep it in the storm for three full turns (though they must concentrate on this like a spell - meaning the party will want to interrupt it if they can, though good luck, as the Kraken has a +16 to Con saves).
Once a day, the Kraken can do a Skull-Splitting Howl, which is a true AoE attack that requires a DC 26 Con save against 10d10 psychic damage for every enemy within 120 feet, and on a failure, the creatures can't concentrate on spells (or powers) until the start of the Kraken's next turn (save for half).
The "fling" ability is transformed into a bonus action, dealing a set amount of damage (I think this is meant to be instead of rather than in addition to falling damage, but I might need a ruling). Finally, it has a reaction called Psychic Reprisal, which lets it do some psychic damage against an attacker, with a Wisdom save for half.
So, the FM Kraken is somewhat similar - it's a gargantuan sea Titan that fights with tentacles (though once again, the art for it makes it look more like a sea serpent than a giant cephalopod). Overall, this Kraken feels like it can pose a bigger threat, though that's to be expected with its higher CR. That said, without the Bite attack, player characters are less likely to be taken fully out of the fight - something that I think is a big aspect to FM's monster design. (There are also, I think, no monsters that stun characters.)
Also, there's a psionic theme here that is absent in the MM version. The Kraken, of course, straddles this line - while most Cosmic Horror monsters are considered Aberrations, much of the Kraken's lore and backstory is built around similar tropes - an ancient being from far beyond the horizon of history, incomprehensibly ancient and often communicating psychically with cultists who might be transformed to serve them (such as Kraken Priests or, from Bigby's, Storm Heralds). In a lot of ways, the Kraken could be used to represent a Cthulhu-like being. But it also rests in that more traditional fantasy realm. (Though let's not forget that they've always mixed a bit - even setting aside Robert E. Howard's friendship with H. P. Lovecraft, even J.R.R. Tolkien included the Watcher in the Water, who is something of an unexplained Lovecraftian horror that is, for all intents and purposes, a Kraken.)
Given that psionics and psychic damage in D&D are often related to cosmic horror entities, that line is drawn even bolder with the MCDM version of the Kraken, while it still retains its Monstrosity creature type.
I find the notion that it can specifically target vehicles - obviously most likely ships - is interesting. While my Triton Wizard is of course very comfortable operating in the ocean, it's actually pretty difficult to grant player characters a Swim Speed (I think the best is if you have a high-level Artificer who can pass around a spell-storing item with Alter Self in it - though this requires concentration, making it tough to use in a serious fight). So, the best option is probably to fight a Kraken from a ship, but this Kraken can destroy that ship if you don't take it out quickly. (Though honestly, I think a Kraken will likely retreat deep beneath the water if a fight isn't going well for them.)
At CR 26, the FM encounter building math basically says you should never face this Kraken before level 18, and it could potentially be a campaign boss fought at level 20 if you have a few fights that lead up to it. I, of course, haven't done extensive testing with FM's encounter-building system yet.
But in terms of true threat, the FM Kraken is hitting harder and with more attacks, and while it can disrupt the party, it's really only taking someone out of the fight by knocking them out (though if it has the range, it can potentially keep melee characters at bay with its Mental Lance).
While the MM version of the Lich runs a serious risk of failing to live up to its reputation through dogged use of counterspell or simply getting focus-fired down, I think the MM Kraken is going to make for a tough, epic encounter (as long as it doesn't get taken out by a spell that can lock it down - though the only real "lockdown" spell with a Charisma save is Banishment, and these monsters typically are native to and stick to the Prime Material Plane - though maybe you've got one from the Plane of Water?)
(Also, as a note, earlier I said the stat block didn't refer to a specific individual, but another reading of the lore actually notes that FM's Kraken is a specific creature from a specific location. Still, I think you're fine using this for any Kraken on any setting, and of course, I think you can very easily just re-skin any named monsters in FM to suit your needs - I was looking at the named Mummy villain and thinking how I'd use her stats for the main "Mummy Lord" in my setting.)