I don't mean to be critical here but I'm seeing a lot of complaining about failed attempt at balance and not a whole lot of comments on the actual content of the Laws of War scrolls.
That said, I agree that it is not a good method of balance. I kind of like the whole "difference in army power" thing, but it is a bit clunky and wouldn't be good in pickup games. I think folded in with a decent comp system "Army Power" could be used as a valid indicator of the difference of strength between two forces, but as it stands in the Warscroll I don't think it works particularly well.
The Laws of War themselves seem inconsistent at best. Some are clearly more useful in my eyes than others, and some will bring the game to a grinding halt to work out its effects (which is a pretty bad thing given this game is supposed to be smooth and streamlined). My initial thoughts are below.
Azyr - Celestial Judgement: Possibly the least powerful unless there's a huge discrepancy in power levels but it could be useful if your opponent fields huge units, or units of models with multiple wounds. Ultimately though it's a one-use nuke that only causes wounds on a 5+.
Aqshy - Flames of Agony: This is one of the better abilities I think. Used against the right enemy it could really boost your ability to hurt them with battleshock tests, and you have the potential to deal mortal wounds to injured multi-wound enemies and finish them off in the Battleshock phase before a test is even rolled. Best part is your entire army gets this and it lasts all game. Really good against multi-wound armies like Stormcast, Chaos and anything cavalry heavy.
Shyish - Vengeful Dead: With a low difference in power levels this is pretty terrible, you could easily be looking at only bringing back 3-5 or so models. You can still make it work though if you use small, multi-wound, heavy hitting units. For us a good unit to combo with this would be Terradons, Ripperdactyls, Kroxigor, Salamanders and Razordons. Any army that's consisted of a lot of heavy Cavalry, Monstrous Infantry, and Monstrous Cavalry will benefit from this quite a lot, but unless there's a big power difference then "balanced" armies probably won't get much out of it. It's a pretty good power if there's a big power difference between armies though - this way you can regularly return destroyed units to the field at a decent strength. At the end of the day though you only have a 50% chance to bring models back, so I wouldn't build a strategy that relies on this.
Ghyran - Breath of Life: I hate this one. The effect has the potential to reduce incoming damage from multi-damage attacks, but the mechanic is awkward and requires a bit of record keeping - which you and your opponent are probably sick of after working out the power difference. It's also utterly useless against multiple Dmg1 attacks, so overall not too great really.
Hysh - Blinding Light: A bit of an old school to-hit modifier for ranged attacks. Pretty straightforwards and could help against range-spam armies (which I'm sure will be a thing). Situational, but you get to see what your opponent plops on the table before you choose a warscroll so it still could be useful.
Ghur - Savage Assault: Another one that can slow down the game. If your enemy makes a 3+ save you can mortal wound them on a 5+. Okay? Doesn't make a lot of sense to me and not a lot of models have a 3+ save so its possible you'll never use it. Arguably the better part of this scroll is that your opponent can only successfully cast Mystic Shield once per turn, and enemy models don't get a cover save bonus if you attack them in melee. Not game breaking but it can definitely help you out against heavy armoured opponents.
Chamon - Magic Ward: Really useful against caster-heavy opponents. -1 to cast for enemy wizards, and your unbinding range increases to 24". This is pretty snazzy because it lets you get in unbinding range of enemy wizards without being at risk of getting Arcane Bolted off (in theory). Not super-powerful, but I think this combined with Ulgu would cause a real headache for Seraphon, Death and Chaos summoning opponents.
Ulgu - Entangling Mist: Not really useful against most opponents I think. When your enemy summons a unit it can only have a maximum 10 wounds in total, and you can "dispel" it on a 4+. Really good against Slann-based Seraphon, who can summon basically anything other than more Slann, and decent against Death armies and Chaos wizards that summon Daemons.
And that is my 2c.