What is the operational advantage of starting an RNAV SID with a VI-CF leg combination?
The PBN manual is the place to start. In Section 5 on departure procedures it includes the following reference:  


  b. Leg type limitations. See Order 8260.46, paragraph 3-1-5 for
  permissible leg types.


Also, all the TERPS requirements also apply, except where modified by the PBN manual.

There's usually no one rule that applies universally. It's about finding the best solution that meets the terrain/obstacle avoidance and meets the necessary airspace and air traffic needs.  I can't say with certainty why the procedure writer made the choices they did, but I can point out a few things that would apply in the SID you reference.  

The 17L/R departure is primarily constrained by the 7000 ft minimum at GISTT. It's there to keep the path within the Class B airspace.  There's a cutout with a 7000' floor around Front Range airport to the southeast. GISTT is located at the edge of the cutout.  It's far enough south to leave room to reach the minimum altitude at the published minimum climb gradient.  The VI/CF is the solution that gets you to GISTT expeditiously.  It also has an intercept angle of about 50 degrees which works well with the FMS and LNAV steering.  

The 16L/R departure has two factors that push it to the VA/DF solution.  First is that it departs over runway 07/25 and there's no intercept (more later), the altitude termination defines when the turn can begin. The reason the DF to MUGBE is used instead of a CF is that there is a 140 degree course change.  You can't have a VI/CF combination with that large of a course change. Thus the VA/DF combo.  If MUGBE (or another convenient waypoint) was better located, a VA/RF leg combo could work but RF legs are relatively 'new' in the RNP FMS world and they aren't very common.