So what's the difference between the two? Why do most choose one over the other?

RH.

one starts with a P and one starts with a D. get it?

And you should have a signature saying "Says captain obvious"

im sorry, i was just kidding, but i used a pcx lens for my adapter. i dont know anything of the dcx. but look at this for a pcx.
http://www.surplusshed.com/pages/item/l3385.html
only $8 total including shipping, and this little peice gets the job done. place it between your gg and camcorder and face the curved part towards your camcorder and you're set. no more hotspot baby! and very bright image.

update, read this:
A DCX, or double convex lens (or concave) can be used for many applications. It converges all light parallel to it's principle axis (meaning the lens is symetrical about it's horizontal axis). It could be used as a condenser or could be integrated as an actual imaging lens.- Aaron Shaw.

maybe this might help.