After spending a week ripping stinky older fiberglass insulation from behind our basement walls, I really wouldn't recommend either for below-grade use -- they both absorb moisture, and the damp old fiberglass, at least, smells so gawdawful it's a living hazard. I used the denim last year in the attic, and it was a dream to work with compared to the fiberglass. Use all precautions of course, but my experience was such that I'll never go back to fiberglass if I don't absolutely have to. You can't add more foam or something else that's mold-proof?

Spray foam $$. Noise, use 2 layers of 5/8 sheet rock w/ rock wool insulation (dense), walls and ceiling. DoD approved. Supply houses or lumber yards, not box stores. Good luck.

Leave it. You dont get any real air flow or temperature transfer to the basement with it out. You will need to adjust current ductwork and fan speed to accomodate the new living space downstairs. I can guarantee if you did take the insulation between floors out and did not heat the basement it would still be cold. There is a slight sound reduction with leaving insulation between. Batt doesnt do the greatest at this but it helps some. Various opinions on this, but fiberglass does help buffer sounds, it is better than nothing. I have loose fill fiberglass for attic insulation and added extra batt around a radon fan in the attic and it has helped. This was before I learned more about different insulation types. The best insulation for controlling sound would be the denim insulation with the strips between the drywall and the framing to stop vibration transfers. There will still be some vibration transfer through the screws but it is significantly less.

Brad, it's not expensive to stop the sound and the noise, all you need is earplugs or noise canceling headphones that would be the best option. It gets expensive when you try to soundproof the room because the sound will travel through most solid materials and it will come out on the other side being as loud. People who do sound systems, or make in-home theaters they have a saying" to soundproof a room, you have to build another room inside it and stop the sound from one room to the other". The reason they saying that, is because the solid materials of one room cannot touch another room directly and if they do, the sound will transmit right through. So when they do soundproofing, the so-called inner room is supported by clips they called RAIC "Resilient Sound Isolation Clips" or they also have something called Whisper clip and they line the walls with a sound absorbing material. There is another way of doing this, but if you looking to soundproof something the system has to be designed, it has to be done the right way and this will cost a little. Anything else, like filling joist cavities, with Roxul, foam, etc will only muffle the sound a little, the main sound will travel through floor joists. If it was so easy everyone would be doing this. P.S Take living space above the garage, you have insulation in every bay, you have a double layer of 5/8" sheetrock, you have 3/4" plywood, you have padding and carpeting on top. When garage door opens, the sound is muffled a little, but you can still hear it in the room as you standing under garage door opener. I hope that explains a little.