Concrete subfloors, both slab-on-grade and slab-above-grade(*) return more energy to the room, especially bass, since they cannot be deformed (flexed) by the sound waves in the air (which uses up energy.) For this reason you might want to do broadloom (wall to wall) or area rugs if you have boomy/tubby problems. A couple of tips:
1. Wool is the best sound absorber (as far as carpet goes) and acrylic the worst.
2. Cut pile better than looped pile.
3. Thin pads with wall to wall, or no pads with area rugs, are better than thick pads. If you need to protect the backside of a very expensive wool oriental rug, use the non-slip rubber netting instead of a pad.
Joisted wood floors tend to absorb sound energy if they have a lot of bounce; especially if they are older, when codes allowed lighter framing than they do now. Unless there are other non-acoustical reasons, I would avoid wall-to-wall carpeting over joisted floors. However, placing thick, cut-pile, wool area rugs in strategic places can be very helpful. These include the floor area behind the speakers, especially with dipoles. The floor area right in front of the speakers if 1.) the woofers are quite close to the floor (or you want to tame a boomy sub) and/or 2.) your listening position ("nearfield" listening) is quite close to the speakers (less than 12 feet).
As for flooring material, unless there is a reason for wall to wall, I always recommend wood to my clients regardless of whether its over a wood or concrete structure. The exception might be an old slab-on-grade with questionable waterproofing under it, but even that cand be dealt with in all but the boggiest conditions.
(*) This applies to high rise steel and concrete construction. It does not include concrete subfloors which are actually just a 2" thin concrete topping over wood construction, as installed in many low-rise condos and apartments to comply with sound control codes.