I think it depends on which (if either) gender is self-closing upon disconnect.
Eg: for air tools and flexible gas lines (LP & NG) you usually have the appliance fitted with the male end and the air or gas supply fitted with the female end -because the female end closes on disconnect while the male end doesn't.
From the link, at least one gender does have an integrated shutoff valve (most likely the female side). Actually, the rather vague wording suggests both might have shutoffs.
If it's just the female side, I'd put that on the supply side. If both have shutoffs, you can do whatever you like.
As for compatibility, I've never read of anyone here using those QDs. Ever.