The cable isn't DVI-D it's DVI-A. DVI comes in three flavors:
DVI-A Analog (more or less vga)
DVI-I Both (Integrated)
The best way to think of it is as two completely different plugs that just happen to fit in the same socket. Where only DVI-I connections contain the information for both. Digital connections are preferred as they allow higher resolutions and a cleaner signal. Analog connections only exist to support legacy (old) monitors.
Now back to your question, will both work. The answer is that the cheaper cable is preferrable, as long as your mobo supports DVI-A or DVI-I, if it doesn't then you need the adapter.