Is this a firewall between units that’s being discussed here?

If he's blowing it in, that's fine. But it sounds as if he's planning to slide batts of it in. That won't work. You need absolute isolation--edge to edge, top to bottom. If there are gaps, sound will get through, just like heat through regular insulation. If you don't have an absolutely tight fit, it's like having the insulation sitting in the room with you--it does no good; the sound (or heat) just goes around it.

We had a rockwool-like material blown into the walls of our 150 yr old house to insulate it. The project was finished by the time I came home from work, and the first thing I noticed was how quiet the house was. We're on the corner of a relatively busy intersection, and now with the windows closed we rarely hear traffic noise.

The rockwool is loose, like soft popcorn, so it can be blown into the spaces between the studs.

I'd give the rockwool a try. The price seems reasonable given the labor involved, mainly in patching the drywall.

Thank you all or the input and recommendations. Sorry for the delayed response, I got pulled down a soundproofing rabbit hole and some work. It seems like the slight increase in noise reduction from adding the insulation may not be worth the hassle. I had a little trouble finding a specialty contractor but I did reach out to some home theater places. The quotes came back around $2,400 which I think is crazy high for a single wall.

@DavidR Thank you for the info on MLV. I had read that adding mass is what will help. Your comment led me to a comparison between MVL and green glue. It seems that the GG has a slightly better rating, but it also a bit more work. I may try to go the route of the Quiet Rock with maybe some green glue or MLV. I definitely don't want to take on the project of building a second wall.

Any advice on a rough estimate of what I should look to pay for two layers to be added and finished? I know this will vary greatly depending on location but I'm in a pretty large city. Also, would you suggest adding two layers of Quiet Rock over the existing normal drywall or should 1 layer be enough? If I simply add one layer how do I make sure I'm off setting the joints if the existing wall is already finished?

From what I can read, Green Glue and MLV are different critters.

MLV can be slapped right up on a wall, and it will reduce noise transmission.

I've often wondered how it would work to put up MLV and then hang heavy drapes over it. Maybe someday I'll try that for a budget home studio.

Nail some furring strips to the wall, hang the MLV, then add drywall over that, and the results are going to be much better. Obviously, that will be more expensive and more involved. It will also look nicer.

A lot of folks seem to think Green Glue is miraculous stuff. I can't say. I haven't actually seen it used. I think it's a relatively new development, maybe the last 10-15 years, and most of the soundproofing work I watched was in the 1980s and 1990s.

Now that I look at it, it seems a bit pricey to me at $45 per 4x8 drywall sheet. But I can't really compare that to what traditional methods cost because I wasn't paying the bills for that soundproofing, my bosses were. :)

I get the impression that it decouples vibration in much the same way resilient strips do. On the other hand, MLV is a sound blocker. Both decoupling and blocking have their place in soundproofing.

I still think your best bet will be working with a contractor who's familiar with soundproofing techniques. A good one should be able to analyze the nature of the sounds you want to block out and select the best material and technique for the job.

But if you're looking for a low cost job, probably any decent drywall hanger can either hang another layer of plain drywall with Green Glue behind it, or a layer of Quiet Rock.

Either way, you're going to have more noise reduction than just rock wool can give you.

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@DavidR Thank you again for all your advice. I'm reaching out to a few places that specialize in soundproofing. The MLV does seem simpler than the green glue. Of course it would be even easier if my neighbors would be mindful of their noise level but that's not going to happen.

@jamesmarcs Were you successful with soundproofing at all? My neighbor's loud truck wakes me every morning so I am trying to find a solution to muffle the loud, cold start. Would be interest in what you ended up using.