Unfortunately I don't think there is a single, right answer for Fixed vs Mechanical. It really depends on what you are comfortable with and what works for you. Here is what is most important to me. 1. Accuracy. 2. Dependability 3. Penetration 4. Cutting (diameter etc.)
That being said, I have had a hard time getting the accuracy from a fixed blade I get out of a mechanical. Even when I get a fixed blade to work "good enough", when I try shooting with bad form (sitting, weight on off foot, stance too open or closed, uphill, etc.) it gets much worse with a fixed blade. Bad form shooting is all to oftern part of hunting I find, but the mechanical blades seem to be much more forgiving in this area. Since Accuracy is my number one goal, I end up with a quiver full of mechanicals.
With my second priority being dependability, I find I have to compromise with using a mechanical as who can argue that a fixed blade has nothing that can go wrong with it? I have found that if you take a little bit of care with the mechanicals, they will be dependable enough. I have never experienced some of the issues others have with mechanicals opening up prematurely or incorrectly (knocking on wood).
Number three is penetration. In my mind, this is a compromise between penetration and cutting performance. I have read many studies in the area and it is documented that penetration goes down as the amount of cutting area goes up (makes sense). Other factors include arrow weight and tuning. All things being equal, I choose a two blade setup for the best penetration. I have a difficult time envisioning a circumstance where the extra slices from a three or four blade setup would help.
Number 4 is cutting performance. Some may put this higher, but I find a sharp blade well placed will do the job no matter what diameter it is (within reason). I am not aiming for the edge of the lungs and hoping for a 2.5" cutting diameter for fudge factor, I am aiming for the middle and am fine with a 1" cutting diameter.
As mentioned earlier, I use mechanicals. I would absolutely change to a fixed if I could get the same kind of accuracy out the fixed with all else being equal. This means field point accuracy in all situations likely to be encountered during hunting. Some guys may be able to do this, but I am not there yet. By the same token, I would prefer someone uses a good mechanical they can hit with than a fixed blade flying randomly.
In the last two years I have hit three elk with mechanicals.
One was recovered after a quarting away heart/lung shot with a blood highway a blind man could follow.
On another I hit the shoulder bone and the broadhead broke off at the shaft. The arrow was found with about an inch of blood on it where the hit happened and the elk was not recovered. It is my opinion no broadhead would have remedied my bad shot (still not sure what went wrong).
On another the elk essentially died in his tracks with a high lung shot where the bull was confused, did not know where to run and just stayed where he was. Broadhead performance was ideal.