Welcome to the .264 shooters club! Most of us are, perhaps, getting a little long in the tooth, but new members are welcome!
Like you, I also recently acquired a new CDL .264, mine is the SF version. From what I've heard, there were only 75 of each made, the blued fluted and the stainless fluted. I haven't shot mine yet either, and I don't know when I'll get to it. It's not a pressing issue with me, I still shoot an old 700 Classic .264 from 1986, which is an extremely accurate rifle.
Also, like you, I shoot a 7mmRM, and in my case, a 7mmWSM. Both of which I like just fine, but that doesn't mean I can't shoot a .264WM as well! I don't think you will notice any difference in terminal performance among these cartridges, they are all in the same general category. The bullet used will determine terminal performance.
Like another poster said, the .264WM is the original long range western big game cartridge. As I type this, I am looking at an original print ad for the old pre-64 Model 70 Westerner. "It makes a helluva noise and packs a helluva wallop", the ad says. "It's most at home in one-shot-or-nothing country. You know the kind of terrain - it's out there where the plains seem endless and where the high sheep grazing seem to flow in and out the clouds. That's where your .264 earns its keep." Kinda romantic, don't you think! At any rate, the old .264WM is a genuine classic, at least among open country hunters. I will always have my .264's.
If you would be a .264WM shooter, then you should be a handloader as well. Factory loadings are limited, basically you have a choice between the Winchester or Remington 140gr. (Didn't I hear Nosler has a new .264 load?). The Winchester load is faster, the Remington load is extremely accurate in my .264WM Classic. Brass is generally available in a steady by jerks fashion. In other words, every so often Winchester puts out a batch, and when it is available, you should buy it, whether or not you think you need it at the time. 7mmRM brass works just as well, but since, like you, I also shoot the 7mmRM, I prefer brass with the correct head stamp.
A recent article on loading the for the .264WM, is John Barsness' "New Powders in the .264 Winchester Magnum", which appeared in the February 2005 issue of Handloader magazine. This article was written because .264 shooters could find very little information on loads using the newer slow powders in the reloading manuals, most of which just have loads for older powders, and haven't been updated in many years. You may still be able to get a back issue from Wolfe Publishing.
Good luck and happy hunting!