With the caveat that I only walked CB, though looked critically at the features... I would have to say there isn't all that much similarity to CB and WH in design. The greens surrounds at CB tend to be wide out and short cut like 6 and 10 at WH. CB in greens size and along with surrounds is just a bigger design. The bunkering is more dramatic at CB and I'd characterize them more like BallyNeal in depth and placements than WH. And, there are the vast waste areas at CB that WH doesn't have. The elevation changes are also more closely akin to BallyNeal than WH it seems to me. CB feels like a course in spacing and configuration that could and will hold big events. It is a big lot course. WH is obviously intimate in that regard.
Degree of playing difficulty would clearly go to CB. And of course for a venue destined to hold USGA events, how could it not be designed more complex or difficult.
Going forward, I think my interest will be in how CB fares in maintaining and holding the fescue turf surrounds of the greens and their firmness. Given the sand capped nature of CB as opposed to the pure sand base of WH, and what I believe is a totally different nutrient requirement given the dwarf blue FWs of WH and fescue dominant at CB, fert applications, I think will be more difficult to monitor at CB. combined with the greater stress of more play at CB, and more fragile FW turf, CB looks to be the more intense management challenge. I believe they will have to top dress more frequently at CB with imported sand, whereas, WH uses its own home sand so to speak. I think it is critical that CB hold on to the intended surrounds playability vision, and should climate and turf evolution of the surrounds fescue species be crowded out and revert to a more poa and high cut and traditional surrounds rough somehow be reverted to, they will be severely compromised in original intent. But, I don't think that will happen as a turf maintenance goal and philosophy issue seems to be the primary focus of the staff.
The super David Wienecke seems to be very fired up to hold the line, and manage the intended design characteristics. He does a great job which he regularly explains on the webpage for CB. (I wish more golf course websites had such a fine superintendent's monthly column). In that regard, Josh Mahar does a fine update column on the WH webpage, and thus the two courses are very similar with top notch superintendents, who communicate very well with the members and users of their facilities.
I just hope I get to play CB once in the next year or so... But if I had to parcel out 10 plays, I'd go 7WH-3CB only because I enjoy the comfort and playability factor with plenty of thrills in the intimate setting of WH more than the the harder demanding and strenuous challenge of CB. If I were younger and a better player, that may go more favorable to CB and even out in number of plays.