FGX is Yamaha's version of the classic Dreadnaught. It's more of a mix of a D and a Jumbo. The CPX is more a mini jumbo of sorts. They both have their own voice in terms of sound.
Both are great guitars, and Yammy has extremely high quality for the price. The CPX is, IMO, the better of the two. Better electronics, better wood, and probably higher construction tolerances.
In the end, if you have the chance, play them both. They'll have completely difference voices.
I played the CPX and the FG730 (dread acoustic, non-cutaway) . I realy liked both. The shop did not have the acoustic-electric FGX
I am looking for something on the smaller side of a dread so it sounds from your description the CPX is more in line
being an acoustic guy like myself (it's all I play), I suggest spending a good amount of time with both. Don't worry about size, or electronics or anything such as that. It's all details that don't matter when it comes down to which one speaks to you best.
I am more concerned about size for comfort. I have a Seagull S6 right now and the wide neck plus full size dread body is to beig to be ideal for me
If you want a thinner guitar check out the Yamaha's series APX guitars. I don't really have any experience with the CPX guitars, but I have a Yamaha FGX and my brother has a Yamaha APX. The APX is more comfortable in my opinion and has better clarity, but the FGX I think has a fuller sound. The quilty of both guitars is excellent.
Dude, you can get a Seagull S6 Slim (which has that awesome Seagull tone, but a smaller more "normal" neck profile) for less than the price of all three you mentioned. And for about the price of the Yammy, you can get the one with the new godin quantum II electronics (which rock).
Well, I honestly suggest D-TAR for any acoustic electric stuff. Search for my praise thread in the sound room, you'll see why.