I think Tom Doak's post above says a lot about how to compare these two courses in a general sense.
I'm also glad to hear that these two courses are ranked #1 and #2 by GD. If GD wanted to flip their positions from time to time that'd be OK with me because I think both courses are great in their own way and I don't give a damn about magazine rankings anyway.
To me the interesting thing about their #1 and #2 ranking is they are such different courses and architectural styles in so many ways, and that despite the fact there is (or was) one small architectural factor about Flynn's Shinnecock that was taken from Pine Valley.
I know both courses well over a lot of years and it's certainly no knock at all on Shinnecock to say if I did a hole by hole match play comparison for my preferences Pine Valley would win about six up.
I say that while admitting that I think I can legitimately find something good and positive to say about the architecture and strategic concept of every single hole on both golf courses. That alone is pretty rare, in my opinion.
In an historical sense, I think Pine Valley's place in golf architecture is more dramatic as it was a course that made an immense impact on the world of golf and architecture right out of the box. Not that it was generally copied but it's hard to deny it made a huge impact on the world of architecture.
I think it's fair to say that Shinnecock grew on the world of architecture to its current status much more slowly over time----which frankly may be the more interesting fact to study and analyze as to why and how.
And I'd add to that there is plenty about both courses that depict their positions at basically either end of the era of the Golden Age----and that fact may be the most interesting of all to study in an architectural sense for such as us----eg looking at the styles of the holes of either course is almost like looking at a microcosm of how the Golden Age of Architecture itself evolved throughout its own era. (this is made sort of ironic by the fact that the course that may've started it all (Golden Age) in America is immediately juxtaposed to Shinnecock and not Pine Valley).
If one thought this means I like Pine Valley better than Shinnecock I wouldn't say that. I admire them both and their architecture a helluva lot but for differing reasons.
For a bonus comparison I'd say both Shinnecock's clubhouse and its relationship to the golf course wins hands down.
Another thing that may be notable is both courses over the years have been not much screwed around with architecturally other than lengthening (compared to some other bigtime American courses). I think that says a lot about both golf courses---or maybe just their clubs.