There could be some misinterpretation here. Variable pitch could be 1) blades or volume vanes that modulate based on an input parameter (e.g., duct static pressure). It could also mean 2) you have to open a panel on the fan casing, loosen some screws, manually change blade angles, and re-tighten the screws.
In general, I would prefer to use VSDs wherever possible. There are drive losses as mentioned above, but the basic fan laws say that if you start with a 50 HP fan and cut the speed in half, the power required will reduce to 6.25 HP (a cubic relationship).
Without diving too deep on this and if I were to make a decision based on current knowlege, I would first fix the blade pitch to the optimum efficiency angle and set the motor sheave to give the optimum RPM at maximum anticipated system flow. Then I would use a VSD to control the fan to maintain the right static pressure in the duct to account for varying conditions.
Gut feel is that variable pitch is a lower level application that could cover up design sloppiness - VSD does likewise, but with more first cost and a more substantial energy savings potential.