why are coilover supensions considered to be a better design than the stoch Honda double A-arm suspension? Aside from the firmness of the springs and the stiffer dampening in the struts is there something about coilovers that is inherently superior to other suspension designs?

 

Coilover refers to the spring shock combo and has nothing to do with the double-wishbones in the suspension.

Some recommended reading... http://auto.howstuffworks.com/car-suspension.htm

And I think you're referring to the difference between MacPherson Strut vs. double-wishbone.

 

So why does having the spring mounted around the strut perform the way it is in a coilover work better than mounting the spring on top the way it is on McPherson strut?

 

The MacPherson Strut suspension uses the strut to provide ride height, shock absorption, and place the wheel. Double wishbone suspensions use a coilover shock-spring combo to provide ride height and shock absorption while the control arms actually place the wheel. This allows for more accurate placement and less change in toe and camber during cornering.