I own both and they have their uses.
On my small slipjoints I still use a fine stone and finish up with paste and a strop. (Actually I try to use the stop most of the time and just use the stone when I have been lazy about touching them up.)
I use the sharpmaker in the same manner with blades made from thicker stock.
After looking at the edge I might touch them up before laying them to the strop.
If I have a lot of steel to remove (either reprofiling the edge or sharpening a knife that has been used for a long period of time between touch ups.) The Apex is tough to beat when considering speed of metal removed and a consistant angle.
If I want a convex edge, I use a phone book on a flat surface and sandpaper. I typically stay on top of convex edges so that touching them up is much easier than trying to re-establish the edge once it has gotten too dull.
In short:
I try to sharpen often enough so that a strop and paste is all I need.
(Of course that is not always the case for one reason or another

.)
On a blade that just needs a little touch up or edge alignment I use a stone or the Sharpmaker, since they are quick to set up and the touch up can be accomplished in a few passes.
If I am reprofiling an edge (I do this a lot on some factory knives) the Apex gets the job done fast and very cleanly. I actually use it most of the time on new knives and my friend's and family's knives since they are usually pretty dull when they "come" to me.
If I had to choose between the Apex and the Sharpmaker that would be tough, but I would choose the Apex due to it's ability to put a nice even edge on a dull blade quickly. It is just a time saver, since the Sharpmaker can accomplish the same thing with a little more care and time.