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I am working on campaign, and I am wondering if the Death World of Kreig: Assault Regiment, is on that same level as the Astra Militarum?

I am forbidding flyers but allowing anything from Stronghold Assault except strength D weapons.

The easy answer is yes.

With your ban on flyers however DKoK Assault Brigade takes a small bump up in power as one of the things they struggled with was fitting in AA as their troops cost so much more.

There are a few things you should be aware of if you are going to have this army in your campaign.
1) Infantry squads do not have combined squads like the AM do. This means orders, Ld abilities, etc. (ie pretty much all the stuff that makes AM good) are less effective. To make up for this the DKoKAB gets two major abilities; Forlorn Hope and immunity to fear and morale checks for 25%+ casualties. Forlorn hope is a rule that comes into effect at 1500+ pts and allows the DKoKAB player to recycle platoons from ongoing reserves once they have been wiped out (the entire platoon has to be wiped, so usually people leave the PCS alive). If you do games less than 1500 pts you will find that the DKoKAB player will have severely overcosted infantry squads and will loose most fights against an AM list.
2) DKoKAB has old rules from before the new AM codex. Thus the rules are the old versions. It is up to you as to whether the DKoKAB player should continue to use the old version or use the correct orders from the AM codex. If the DKoKAB player uses the old rules they will struggle mightily with all the jinking skimmers in the game now. Usually this is not a huge deal until you start having them fight against CWE or DE where their lack of ignore cover on anti tank weapons and fast assault units equals out to incredibly survivable eldar.
3) Be aware that DKoKAB can take rapier las destroyers in the elites slots and field artillery in the HS slots. A lot of people are not aware so it is a common question I get when people see my army. (ie How do you have 6 artillery units?)
4) The allies matrix in the army list is different that the standard imperial bro chart. IMO this is no longer the RAI but it is definitely the RAW.
5) If they bring a full platoon of death riders they are full of win no matter the game result. I love those models.
6) The CCS pays through the nose for lots of useless rules and gear but they have engineseers which can make a single weapon +1 Str against vehicles. You will want to decide whether this stacks or not but it can be pretty nasty on a leman russ punisher or some of the LoW.

Good luck with your campaign. If you are letting DKoKAB lists in then at the very least it is going to look great.

Thanks for the response.

I am only going to allow and IG, DkoKAB and Stronghold Assault books. And there are no other factions involved.

Do you think dropping the IG book to the previous edition would help? Or is the difference negligible?

It's hard to say. You clearly have a campaign system in mind that heavily restricts what players can take (no flyers, no non-IG factions, etc), while most power level analysis involves playing the entire game as-is. I don't think you're going to get very much useful information about such a unique situation, simply because nobody else has ever played games under your rules or put much thought into what strategies they would use in that situation. If you want to at least start the discussion you should first post the complete rules that your games will be run under, including things less-explicit expectations like "don't take too many tanks" or "the IG player should always have at least one conscript squad for fluff reasons".

Sounds like a campaign Swastakowey would like.

Sounds fun, Guard on Guard always looks great on the table and is a lot of fun to play.

Thanks for the responses.

I have not finished writing the rules, but here is the cliff notes each player is fighting over a Risk map. One army per 3 territories, each territory is wroth X pts. The points can be spent to increase an army size up 2k, or to purchase another army or the build fortifications up X pts. on a specific territory.

Aside from was was listed earlier there no other restrictions.

That sure how that helps, but my overriding concern is a player is going steam rolled because,one codex is better then the other.

The DKoK AB list is capable, but has nowhere near the flexibilitty of a basic codex list, especially with the older IG codex orders and leman russ tank costs, as well as an overly expensive chimera option, but can play as long as its strengths are adhered to.

It sounds fun.

It also sounds like I cannot give you a definite answer. I think they should be pretty close in power level but it is going to be incredibly dependent on what the players are bringing and if they need to capture forward objectives. A lot of the craziest stuff the AM platoons can pull is limited by the loss of ally options.

Funny enough IMO the power levels between the two armies will depend heavily on how prevalent ruins are. The AM list has the wyvern which is better against units in ruins than the thudd gun (IMO the carcass shells mortars are not as good as wyverns). Alternatively the DKoKAB might win solely through attrition due to the Forlorn Hope ability keeping them on the board. Either way these fights are likely to be incredibly bloody with pie plates flying around across the board.