I don't know what you have planned for LH, but I am going to list all 10 factions, what I'd change, as a rough idea.  

Altar:  I don't play them all that much, the whole henchmen thing turns me off, they just scream OP.  

Henchmen: I'd make them a spawn, with a cap of the number of 5th lvl heroes you have.  You get one, they perma-die, but a new lvl 1 henchmen gets spawned a short time after, random chance each turn of a new one spawning.  Henchmen would get a XP bonus from being in a stack with a champion.

Swords: I like the swords.

Quest maps: Good idea, but think this should probably be an auto-spawn as well, and not something you purchase, related to fame.

Pariden: I like them for the most part as they are now.  I do think their shard bonuses scale to map size pretty heavily

One change: I'd change their Leht Staves- make electric staves avaliable to all factions (two strengths), make Pariden the only faction with a generic magic damage staff.

The magic damage staves would benefit from spell mastery (so champs would have a reason to use them), and maybe life/death shards would add to their base damage.

Gildar: I don't really play them much due to the tactical magic damage penalty.  That penalty is necessary though, they are super-buff otherwise

I'd  keep them mostly as is.

Tarth: Rebels is a harsh penalty, often chokes them out, but is part of the flavor. With unrest being linked to cities in LH, I do wonder if Tarth will end up being really hurt by this.

One thing I'd like to see perhaps is diplomatically, they tend to have better relations with empires, and worse with kingdoms.   They should in particular hate Capitar and vice versa.

Another idea: take rebels away, but give them a penalty to fighting in groups (increased cost to make groups/squads/companies), but give them an extra building that acts as a barracks that can be put anywhere.

Capitar: I like the idea of them being a mercenary/cavalry faction:

I'd increase maintenance costs of mounts heavily, this would allow Capitar to be hurt less by mounts.

Resoln: I think the dodge benefit is nice, but a bit OP.   Without it, they're underpowered.  I'd change the mechanics around to their blood trait (they'd get a flat -10% hp, but 1 spell power, 1 defense, inability to wear any leather/chain/plate, and 2 spell resistance per level)  They can wear robes.

I'd give resoln some unique robes.

I'd also buff the elementals that come from stronger mana shards, elementals are paper-thin by end game.

Krax: betrayers is a neat concept, but there are some problems:

The first problem is life magic heroes can never benefit from shards.  Easy solution: give them a unique shard that works as a life and death shard simultaneously.

The spears are neat.  A Javelin that melee troops could throw would be flavorful, one per battle, decent damage

I'd keep silver tongue influence for cities, but change it for troops to make bribing of troops with gold.   Bribing would be influenced by relative influence, and relations (the more negative they are the harder it is)   This would encourage gold hoarding. 

Unique building: Jeweler.  Gives gold and influence.

Magnar: they're pretty annoying with slaves, but slaves are just too damn common for troops.

I'd have slave troops increase  global unrest for 1% for each slave troop created, to encourage Magnar to use regular troops, and maybe higher penalties for having more cities (this would scale them towards smaller maps though)

Perhaps give Magnar to compensate some special unrest reducing spells/buildings, at a price.  (I think enough of these buildings exist), but in large maps, global unrest reducing buildings would help compensate.  Maybe make it later-game tech to balance it out.

Yithril: interesting faction, but overpowered

Why do they have militia archers?

I would give them throwing axes is part of their axe tech- a better throwing weapon for their melee troops. 

Urxen: I'd make them vuln cold resist fire, to be a counterpart to Magnar.

I'd give them a bonus to groups, their groups/squads/companies would be cheaper

They would also gain a dodge bonus in rough terrain (If the hex they are fighting in costs more than 1 to move into like a forest, they could get the bonus)

I'd also give them an inability to use mounts period (as part of their blood, due to their size) , but they could make horse/warg resources into food.