Which adjective should come first, modular or versatile?

Native English speakers... I hear the order of adjectives is important, and getting this wrong is jarring to read.

I'm making a pitch to upper management about building a "modular and versatile thingamawidget". Or is it "versatile and modular thingamawidget"?

If it doesn't matter, I think I'll go for the latter, as it abbreviates to something easily pronouncable without sounding like a paramilitary group or a ride sharing business.