The table below shows prices per month for 2 storage level, 50 GB and 100 GB, which are what Dropbox offers.
You will see that Amazon prices Cloud Drive storage at lower prices than Amazon S3. Dropbox use Amazon S3 with standard redundancy as the storage back-end. So, unless they get special prices from Amazon, they will never be able to complete on price with Cloud Drive. This is exactly what Amazon is aiming for with their pricing, I believe.
Note that Amazon S3 also offers Reduced Redundancy Storage (RRS), which interestingly is priced very similarly to Cloud Drive. Does that mean Cloud Drive uses RRS? (99.99% durability, instead of 99.999999999% durability) We don’t know yet. But it would be a bad surprise if it does.
Currently, Cloud Drive is only accessible via web, and thus is not yet as widely accessible as Dropbox. However, this could change very quickly if Cloud Drive API is made available or if Amazon releases their own client for PC/Mac/Linux/Mobiles.