What is the advantage of the blisk design in the new Trent XWB engine?
Since the blades and rotor disc are a single piece, there are no additional fittings (bolts, screws etc) to attach the blades reducing complexity and weight.  The blade root joints are also a source of failure through manufacturing defects and fatigue cracks.

The disadvantage is that any damage to a blade requires the entire assembly to be replaced rather than a single blade.