Acoustic panels are usually used to adjust how a room should sounds, to tune his tone and control its reverberant field.
If you need to improve sound proofing, you must think in terms of increase walls/floor/ceiling's mass. Drywalls are an efficient way to gain mass and keep highs and mids trapped in the room. Efficience will depend on how carefully you cover inside surfaces.
Remember that any thinner wall will be where sound will drain out, as windows and doors (one weak ring in the chain is where all our efforts will fail). Opting for double pane window, thicker and heavier glasses and doors, will help. Avoid openings below doors or even keyholes, you would be amazed how much sound energy can escape by such tiny openings. In studios, people use neoprene rings to seal doors and windows when closed to their backstop. If air can get out, sound will too.
Unfortunately, lows can put things shaking too easily, so it is considerably harder to inprison them. As they get out by vibrating walls/floor/structure, you must get ways to decouple inner isolation from outer walls. You can hang drywalls on metal trails, reducing its contact points to the wall, or use wires to suspend them on the ceiling. There is even kinds of hangers that have rubber cushions to help dampen vibrations.
There are many ways to isolate sound, but sky is the limit. Consider how much you intend to spend and how much sound proofing you need.
