FOGOLD, I'm pretty certain you should be able to do both. At least that's what I'm doing.
AH allows you to program Direct-X buttons directly from inside AH. So that means that in the FOXY programming app, you need to designate those buttons that you'd rather program directly in AH as Direct-X buttons.
I can't rember the syntax offhand, but it's probably something like:
Set S3 as DX4 (which will designate button S3 as Direct-X button 4).
Then when you've done that inside of FOXY, you can go right into AH in the stick mapper and program those Direct-X buttons.
This is how I setup my views in AH on my Cougar. In FOXY, I designated hat 3 to be the POV hat #1, then I went into AH and programmed POV hat #1 with 8 views.
Hope this makes sense. Here's a link to Cougar World that has a whole bunch of info on programming the Cougar.
http://cougar.frugalsworld.com/