I've been reading up on this lately since I have a huge amount of claro walnut incoming on my new URB. The basics are that there is a bit of confusion over just what constitutes Claro, since it can vary depending on the source. It does seem to be more West coast and may have some grafts of eastern walnut species. When I go pick my upright in a few months I will be visiting the shop and want to ask my builder, Nick Lloyd, more about claro and where he gets it. I know he's crazy about it and has a stockpile since he needs lots of it to build even a single bass.
From what I've read, tonally, claro has a more open, porous texture that gives a little bit different tone than the dense, deep and articulate sounding walnut from the east. I spoke with my local classical guitar builder/luth about it, and he loves the stuff.
I think the sound of the famous Fodera users with walnut bodies- Garrison, Janek Gwizdala come to mind- have a good example of what the eastern walnut sound is like. Very distinct. I want to hear McBride's new fretless since it's got tons of walnut. I had Ken Smith Black Tiger Presentation with a bunch of crotch walnut, though the bass had a lot of other factors that contributed to it's sound, but to my ear there's something similar to that bass and say Janeks.
I don't think Fodera uses Claro on any body woods, and like Jason was saying, it probably doesn't impart a high tonal variation as a top vs eastern walnuts, so it's probably a mute point. I like the look of the crotch walnut a ton and will likely just go for a piece of that for my top when the time is right.