Spent some time analyzing the various battalions (used Serenes Forest initial stats+level up gains, as there aren't Level 5 stats), here's my summary:
One of the main takeaways is that most of the endgame battalions are in B - A gets access to a few better ones, but that's it. Meanwhile, the lord battalions at C are crazy strong and come extremely early.
Battalions are huge stat sticks - stats like 8 physical attack or 5 prot/7 res amount to 20% or more of your natural level ups, which makes getting to B authority very worth it. They are incredibly strong.
What it also means is that characters with good proficiencies (who can hit their class requirements faster) are better, because they can hit their authority ranks faster and get the best battalions sooner. Also relevant because bows are really strong.
Even for support units, it's relevant since some of the best gambits like stride/retribution are authority rank locked.
How I ranked:
Physical Rating Phys+Prot+Res+Hit/20+Crit/5+Avo/5
Magical Rating Mag+Prot+Res+Hit/20+Crit/5+Avo/5
Basically saying 20 points of hit, 5 points of crit, or 5 points of avoid = 1 stat point otherwise. Mostly ignored charm. I may want to re-evaluate, as crit/avoid scale well late game (e.g., 10 points of avoid=2 stats if you're about to take 20 damage, or 5 points of crit=15+ damage if you hit a crit) and are non-linear in some ways (e.g., going from 80 to 90 dodge is bigger than 0-10 since you can more much confidently dodge tank - this is even due to hit formulas (90 hit is significantly better than 20 hit due to how it's calculated)
First calling out these, as stride is damn good
Seiros Holy Monks, Kingdom Calvary, Gautier Knights - notable here that Kingdom Calvary is for BL and Gautier Knights requires the Sylvain paralogue, if you want more.
*These are pretty bare bones - however, you can usually get some decent stats out of them, and Jeralt's Mercenaries are low key really strong
Jeralt's Mercs: 3 attack, 10 crit, 15 avoid. *f you don't rank up authority, this is really good. Endgame, 10 crit and 15 avoid is worth *a lot* and it just becomes a cichol wyvern or other A/B level battalion without as many stats
Alliance Duelist: 9 crit, 10 avoid. outclassed version of Jeralt's mercs
Kingdom Calvary: 4 atk, 5 hit, 4 prot decent starter stat stick
Alliance Mag Corp: 3 mag, 10 avoid, 4 res
The ones here aren't super spicy and most are pretty similar, but a few stand out because they pack both Prot and Res. Also the first flying battalions for peg knights/wyverns
Kingdom Pegasus Co.: 4 atk, 5 hit,5 avoid, 3 prot, 4 res
Alliance Peg Co: 4 atk, 5 hit, 10 avoid, 2 prot, 3 res imo the strongest choice with 10 avoid
Empire Peg Co: 4 atk, 15 hit, 3 prot, 4 res
Empire/Kingdom calvary: 4 atk, 4 defense, some hit/avoid
Alliance Magic Corp: 3 mag, 10 avoid, 4 res
Where it gets spicy. The Lord battalions are busted and comparable/better to most A and B rank, but a few others stick out as solid (Holst, Vestra). Lord battalions also get 12+ might gambits, which when paired with high strength, can deal some insane damage
King of Lions Corp: 10 phys, 5 hit, 15 crit, -5 avoid, 5 protect Probably the ultimate C battalion in terms of offense, and one of the strongest offensive battalions period
Holst's Chosen: 7 atk, 5 hit, 5 crit, 7 prot Arguably the best non-lord C battalion for physical
Immortal Corp: 8 atk, 15 avoid, 4 prot Might even be stronger than King of Lions late game thanks to the avoid - also easily the strongest flying C battalion
Supreme Armored Co: 7 atk, 6 mag, 5 hit, -10 avoid, 6 prot, 5 res The worst lord battalion because of that -10 avo - in general, kind of eh because of it. I rarely run it.
Empire/Golden Deer/Kingdom Wyvern Co: 5 atk, 5-15 hit, 5-10 crit, 4 defense Solid stat sticks for C
Vestra Sorcery Engineers: 7 mag, 10 avoid, 4 prot, 6 res The single best mage battalion, but also the tankiest C battalion
Morfis Magic Corp: 5 mag, 2 prot, 5 res Alt mage battalion but you're better off running stride on the rest of the mages
Endgame quality battalions really start at B, and actually make up most of the best ones. Many are better than A rank battalions
Goneril Valkyries: 8 atk, 20 hit, 15 crit, 6 prot, 1 res second highest rated battalion, but 20 hit is probably not as good as some avoid (see A rank Cichol Wyvern)
Galata Pegasus Co: 7 atk, 5 hit, 10 avoid, 5 prot, 6 res 2nd tankiest battalion, available at B
Brigid Hunters: 4 atk, 10 crit, 20 avoid - might be the best for dodge tanks - 20 avoid, 10 crit
Fraldarius Soldiers: 7 atk, 20 crit, 6 prot crit monster, although probably outclassed by Black Peg or Cichol wyvern
Gautier: 6 atk, 20 avoid, 5 prot strong avoid option, but Brigid hunters trades 5 prot for 10 crit, which is probably worth it if dodge tanking
Empire Elite Wyvern: 8 atk, 10 crit, 6 prot standard stats, probably the best buyable B
Holy Knights of Seiros: 7 atk, 5 prot, 7 res Another very good one to buy at B, very tanky
Duscur Heavy Soldiers: 8 atk, 5 hit, -15 avoid, 10 prot
Golden Deer Calvary: 8 atk, 5 hit, -5 avoid, 7 prot, 2 res
Leicester Mercs: 7 atk, 20 hit, 15 crit, 4 prot solid offensive choice
Alliance Master Archers: 4 atk, 15 crit, 10 avoid,4 prot
Gloucester Knights: 6 phys, 6 mag, 15 hit, 5 prot, 5 res A very well rounded choice
Empire Holy Mag: 6 mag, 4 prot, 7 res probably the second strongest mage choice
Hervring Prayer Troops: 7 mag, -10 avoid, 4 prot, 6 res
Macuil Evil Repelling: 7 mag, 30 hit, 1 prot, 6 res
Once you get to A, you actually don't pick up that many super strong ones
Black Eagle Pegasus Co: 7 atk, 10 crit, 10 avoid, 5 prot, 7 res the highest rated battalion by my equation, thanks to the mix of offense and defense
Cichol Wyvern Co: 7 atk, 15 hit, 15 crit, 5 avoid, 6 prot, 1 res similar to Goneril but trades some hit for avoid - probably a bit better
Black Eagle Heavy Axes: 7 atk, 10 crit, -10 avoid, 8 prot, 2 res
Golden Deer Calvary: 8 atk, 5 hit, -5 avoid, 7 prot, 2 res
Indech Sword Fighters: 8 atk, 20 hit, 10 crit, 4 prot decent offensive choice but not super amazing
Blue Lion mag: 7 mag, 5 hit, -10 avoid, 5 prot, 7 res outclassed by Empire Holy Mag at C
To be honest, the rest of the A's, including Indech sword Fighters really, are not particularly standouts.