Great question, and one I've thought about a bit myself.
Obviously, Streamsong and Bandon Dunes, both public, are the best places to help define this. When Gil's Black course at Streamsong opens and should he be able to finish a course at Bandon, this will be a far easier to observe in real-time. On the private side, I'd offer that Sand Hills & Dismal Red, and Friars Head and Sebonack provide fertile grounds for comparison as well. A few of us (along with the non-architecturally-centric) have been fortunate enough to play Boston GC & Old Sandwich back-to-back as well.
When I ask my wife or her friends, as well as my playing buddies (non GCA-focused) to tell me what differences they see between C&C and TD's courses, invariably the first part of the conversation turns to the greens and their degree of undulation and difficulty. I believe most people feel as if both build "different and interesting" greens, but most I know also feel as if Tom's greens are considerably wilder and usually more undulated. The words I've heard used for Doak greens are "crazy," "wild," and "goofy in spots," whereas the adjectives for C&C are "nuanced," "more subtle" and "tamer." I think most who've played BGC & OS, find Gil's work more similar (site specific) to Toms, but the BGC land seems to have sharper elevation shifts on a tighter property than OS in general. Personally, I really enjoy all three and find it easy to interchange those adjectives for all three designers on different holes. I think the general golfing public does notice those differences, especially when they've been fortunate enough to play both designers inside a short period of time.
I'm not sure they notice any significant differences in routing, strategic variety, or mix of golfing adventure. All three present significant width, and strategy, all while preserving critical angles and lines of charms. The minimalist school seems to adhere to these principles wherever they have the chance and I'm not sure most golfers would discern the differences nor the subtle variety in bunker placement and aesthetics.
I do find that golfers who've historically remained indifferent to architectural styles will naturally lump the above trio into a single group, despite even affirmatively noticing the variance of their greens-shaping.