I've never purchased a CD from DeepDiscount but I've generally found that their DVD prices were lower than Amazon--sometimes much lower. But I mostly buy from Amazon because I have the deal where all two-day shipping is free. DeepDiscount is also free, but always longer than two days.
It doesn't matter to me how long it takes for me to get something, as long as I get it...so I'll almost always go for the cheaper price. Of the DVDs that I've purchased, there have been a few (very few) cases where Amazon has lower prices.
As for what used to be DeepDiscount
CD.com, about half of the orders that I've placed with them were cancelled without any notification to me! I would place an order and everything would be fine, but then they would never take my money. I'd go and check on the order status and it would say "Complete"...I'd go into the specific order and everything would show $0. And that would be it. Nothing else.
So, I rarely ever ordered from DeepDiscount
CD.com, but the DVD side was great. Hopefully, now that they've combined and have a lot of other items (posters, storage, etc.) the DVDs will still be fine and the CDs will be better.