Firstly a dbox and dreambox are two differents things; the dbox is the cheaper model, and the dreambox is the more expensive one.
Your Pace box and dreambox basically both do the same thing (they receive the same channels), except the dreambox is alot more powerful; alot faster; and generally a much nicer box. You also dont need to play around with BKs and IRDs etc. The dreambox can also connect to internet and play games etc.
A dbox is very similar to the dreambox and can do the exact same things, the only difference is the price and the age of the receiver. Some dboxes are now 5 years old, whereas the dreambox is a nice new shiny model.
The only dreambox that works on cable is the DM500c.
The nokia AND sagem boxes both work on cable.