Thats a lot like asking whats the best broadhead...or whats better Chev or Ford...lol
The main reason for a stabilizer is to prevent pin float and make that pin more stable and allow a proper follow thru...
Old school rule the longer and heavier the stabilizer the more stable or steady...
Noise is an after thought when it comes to stabilizer..even thou they do reduce hand shock and vibration...there are other factors that can be done to eliminate or dampen noise...
Although most today regardless of size have vibration dampeners capibilities which in turn reduces noise...
Pending on what one wants to do...you said to hunt...so most dont need much more stabilizer than the 6-7 inch you mentioned...
Since your hunting if you can hit the heart out to your proficient/efficent range using none or a small stabilizer... that should tell you whats best...it doesnt matter where in the heart you hit em...
I use a 4" Axion stabilizer that has the Mathews Harmonic Stabilizers HS and dampeners in it...they come in a heavy weight and a lighter aluninum HS...I choose the lighter ... dampens noise and I can shoot as well with it as a 6 or 7 inch stabilizer that I dont need for weight or a bush catcher...
The longer than riser/sights stabilizers [stick way out from the bow] will work perfect in blinds or stands...however if you hunt elk or deer on foot and find yourself "in bushes where the rabbits wouldnt go" then a short stabilizer is the best...
Borrow a couple different sizes and shoot them...go as short as can to where it starts to effect your shooting and find the right size...
JMHO
Neil