We have both in close proximity. BB seems to be busier any time I am in there vs. CC, and the BB store is in much better shape as well. For example when I was shopping a medium-grade HT system this past spring (~$5K range), when I wanted to check out the best system CC had half the speakers weren't working in the "HT" setup they had and no one could get them working either. After I finally got a salesman to wait on me, he blamed it on the "cryptic 3808 Denon receiver that no one could understand" - great sales technique there! And that's where they also had their best Polks and BAs connected. Result - no sale to me! (Next time I went in, that whole HT area had been converted to shelf stock!) CC is more limited in product areas covered as well, like no appliances. Conversely, the sales team at BB is always available and mostly competent, and the store seems to be well laid-out and "operational". My only complaint with that particular store is it's too loud in there!
When I'm "in the market" for something I will check both stores, but quite often end up buying from neither. For many items we also have local "Mom and Pop" stores selling identical items, and they will often price match. As one local M&P store also has our area's only local authorized service center for many brands I feel a need to help keep them in business, so I will funnel as many retail purchases to them as I can. The only problem with the M&Ps is that they don't have the depth of product selection, or in many cases "one stop shopping", otherwise I would have little reason to venture into either of the big box stores.
As I look back over my "durables" spending in the past 5 years or so, I have made many purchases at BB and only a few at CC. But for the most part they have all been $200 or less at a time except for one HTIB I bought at BB for about $500 and a Mag Monitor for about the same price when LCD displays were that expensive. I buy some disks and accessories at BB, but little else. The bulk of the ~$15K I have spent for HT equipment over that time has been spent at M&Ps.
I will be interesting to see how all of these survive the economy over the next several years. I'm guessing BB, and maybe one M&P with a niche will be the only ones to survive...