Blood Hunter vs Hexblade Warlock

For an upcoming campaign, I was thinking of playing a melee damage dealer and was looking at the blood hunter, specifically the Order of the Mutant. I thought the idea of potentially having 25 Strength, Crit on 19 to 20, and regeneration to be awesome. I was thinking of going Half-orc and using a Great Axe to really dive into doing insane damage when I crit. For a 4th mutagen, I was considering cruelty to gain an extra bonus action attack to increase it further.

I can't remember where but I remember reading though the Hexblade warlock kind of surpasses the Mutant Blood Hunter and I was curious are there any benefits to still going Blood Hunter or is a Hexblade warlock superior?

I do like getting booming blade, and Melee and Spell attack stat being the same. It looks like it would have similar features. I would also consider a multi-class into Stone Sorcerer so I am 2 stat dependent.

I guess I have the following questions and feel free to link a former thread if it already covers this topic (I couldn't find one with my weak google-fu):
1) Strengths and weaknesses of the Blood Hunter vs a Hexblade Warlock
2) If Warlock is hands down better, what would be a good balanced multi-class with Stone Sorcerer?

This is a home game and open to most UA material with some exceptions (looking at you Lore Wizard).

I had to google Blood Hunter to know what it is, so I'm not going to be evaluating it too much. Hexblade Warlocks though I can talk about and they they really aren't considered damage kings. Not putting it down, but it usually wouldn't pop up in a discussion of the top three classes.

It looks like you're going for melee damage and survivability as your rating of awesome considering the BH abilities you talked about. Paladins and paladin/sorcerers play really nicely in that space. Barbarians as well. What levels are you likely to spend most of your time? At the very least we can suggest things that you can compare against the Blood Hunter.

Well this will be serving as the off-campaign to our normal 3.5 group. One of the players wants to give the DM a break after our 3 year campaign before starting part 2. He plans on running us through Curse of Strahd and then Tomb of Horrors afterwards potentially. I see this as a character which may eventually hit 20 (if he survives) but it would be a long road. Main levels to consider would be CoS and ToH. We would start Strahd at level 3.

I was thinking of trying something new. I have played a barbarian before and a sorc/paladin.

The damage contributors for Order of Mutant Blood Hunter is using different "potions" to give temporary abilities. By lvl 18 you have 1 permanent and 3 temporary. Every potion brings a disadvantage with it. The idea was Half Orc, 25 STR, 2-3 attacks (extra attack and BA attack), Great Weapon Master, Blood Hunter Blood Rite (and extra scaling damage die, d10 by lvl 18) and expanded crit range 19-20.

The damage for each hit if GWM is used would be 1d12+17+1d10. They also have access to curses, 1 doubles the damage dice for the curse making damage 1d12+17+2d10. If I crit it would then be 3d12+17+2d10 damage.

The warlock/stone sorcerer combo is one where I like a lot of features from both and am unsure what might be the best division for some damage, some tankiness, and lots of teleportation (stone sorcerer aegis)

I know BH damage is broken unless you use the 1.8 newest version. It is a lot more balanced.
That being said I still think the BH would be higher damage unless you are using the Warklock smites from UA.

Yeah I would definitely pick up the weapon smiting invocation and using booming blade or green flame blade for attacks.

Damage would look something like 1d8+5(CHA)+3d8(booming blade)+6d8(Eldritch Smite with max warlock spell lvl)+1d10 (Hexblade Curse) damage crits on 19 or 20. If I take some sorcerer for quicken it could be done twice, though the rider on booming blade would not double on if I chose the same target.

EDIT: Also, the Blood Hunter numbers are from the 1.8 pdf. That really makes me want to look up the old pdf and see how insane they were.