That's a good question, because the CCleaner free space wipe isn't documented in detail, so comparisons are difficult to make. The CCleaner function seems to run very quickly, which suggests to me and Joel that it does not work in the same way as Eraser. Almost certainly, CCleaner does not wipe cluster tips (which, in my opinion, is not necessarily a huge issue), and it doesn't offer the same range of options as Eraser.
As both programs are free, you can use both, which I do. A CCleaner wipe will be much better than nothing if time is limited, but if you are selling or disposing of a computer or drive, Eraser (in my view) provides a greater degree of documented security.