AcoustiPack is thick enough to be able to absorpt soundwaves and has also heavy layer... light and thin Akasa can't really neither dampen vibrations or absorpt soundwaves and should be put only to places where you can't fit better materials.
Also BeQuiet makes mat which has ~2mm thick heavy vibration dampening layer and ~8mm soft layer so I would recommend either AcoustiPack or it because dampening vibrations is very effective compared to trying to absorpt only soundwaves. (as lighter material aluminum picks up vibrations more easily)
Lian Li A71 is very good from noise aspect because HDDs are soft mounted, it doesn't have overhyped holes in sidepanels and there's door which blocks direct noise escape path (sound looses intensity everytime it reflects) so in that case these can really help to make it few dBs quieter. Unlike with some most widely (over)hyped cases.
Normally cooling realies nearly completely on airflow so as long as that doesn't change effect to temperatures is minimal. (especially compared to what screwed up airflow design can cause)
Of course sound absorption materials would work best if you blocked all holes to "outside world" but that would prevent cooling, also door blocking direct noise escape path in front lessens criticality of that.