I recently read an article published in QDMA on broadhead choice. Read it here.

https://www.qdma.com/does-broadhead-choice-really-matter/

Today the use of mechanical broadheads is more widely accepted among many Compound Bow Hunters and work well as evidenced by the article. Many years back the mechanical broadheads sometimes failed to open or open all the way and consumed energy needed for penetration.

Mechanical designs are better today, however still consume energy to open and must be inspected as they age in your tackle box.

Traditional longbow and recurve hunters still like fixed blade cut-on-contact because it replicates what our early ancestors hunted with. And that includes making your own razor sharp arrowhead ( even stone arrowheads) and hunting with it where legal.

That said; Here in New Hampshire a bow must have a minimum of 40 lbs draw weight whether it is a compound or a stick bow.  It takes a bit more energy to puncture the hide and open the mechanical broadhead then does a cut on contact broadhead.  If that is true, and I believe it is, then when shooting a lower draw weight, I would be apt to shoot cut-on-contact traditional broadheads so that all the energy is used for penetration.

If all of us were shooting compound bows of a  draw weight to guarantee the opening of a mechanical head then it makes no difference as long as the cutting width of the blades are within the limits set by your state.  In New Hampshire the rules are no narrower than 7/8 inch or wider than 1 1/2 inches; See below.

http://www.eregulations.com/newhampshire/hunting/deer-hunting-regulations/

I still like traditional cut-on-contact heads as they are works of art too.

Good Hunting!