What the unibody has going for it over the body-on-frame construction is torsional stiffness, which helps the engineer obtain better handling. Because the frame (unibody) is stiff, compliance can be designed into the suspension. It will also be tighter, which usually means fewer rattles and creaks.
As Kewl said, the downside (compared to a real truck) is load-carrying ability. I just don't know what a frame-on-frame design is
Another small point: the unibody is not a chassis, it is a frame. The chassis starts with the frame and includes the suspension and other bits.
The unibody is a modification of the monocoque, a design where all body panels are stressed and constitute the body and frame as one. A unibody has a central structure that is all welded, but there are some panels that are then bolted on.
A unibody will generally be better for the passengers in a collision, as the entire frame structure can be designed to absorb the impact. The downside is that since it has been deformed in a collision, it is more expensive to fix. Not impossible, with the right equipment, just more expensive.
While each design has merits, the unibody is more suited to a performance oriented road vehicle, and the body-on-frame construction is more suited to an off-road vehicle or a truck.
Incidentally, having the unibody design is one of the primary reasons why the trailer hitch is so expensive for the X5. It is easy to make a hitch for a vehicle with a separate frame, it is harder to make one (correctly) for a unibody design, particulary when you are dealing with the 6000 lb tow limits of the X5.