I've played both frequently (over 6X each), most recently back-to-back this October.
Hidden Creek was long my preference, and agree with Jim that it's architecture is more conducive to fun. It's routing is more certainly more intimate and walking friendly, but it's property(sandy pine barrens.....no preponderance of wetlands or swamp) lends itself to well to an easier routing. My hats off to Roger Hansen and ownership for encouraging Bill & Ben to successfully re-create a heathlands-style course on US sandy soil. It is a warm and low-key club.
Galloway is a wholly different animal and should be treated as such. It is to Hidden Creek, what apples are to oranges or Van Gogh is to Cezanne. It's big, challenging, a maximal design, more aerial and less intimate than HC. That said, it is impeccably maintained, plenty wide off the tee, beautifully bunkered and equally a blast to play. More exacting for shot-making surely, but no less fun as areas have been opened up over the years and new tees have allowed for shorter players to find their fun quotient without any brutalistic forced carries.
In my opinion it's one of Fazio's better designs and the routing, while not the coziest of walks, likely evolved from the inherent difficulty of having to use, and connect, different tracts of land ranging from sandy soil to swampy wetlands. There's very little chance the State of NJ would permit a course of it's scale there today. Surely, Faz moved some dirt while building it, but it's not as egregious as many other works of his.
This past October in NJ was glorious by every count, for growing and maintaining firm turf grasses, yet HC played demonstrably slower and softer than I ever seen before. Ground game shots that would normal chase onto greens didn't and green speeds were noticeably slower than I'd ever seen there. Playing strategy needed adjusting and it was perplexing? Our caddy mentioned that the course was much softer and slower this year, yet couldn't tell us why? Next day, in a steady drizzle, GN played plenty fast from fairway through the greens and it produced a distinctive contrast from the previously sunny day at HC. I was so pleased by the firmness that I stuck around after the drizzle disappeared and played another swift 18.
Both are special IMHO and aren't easy nor fair to compare heads-up.