The 2 speed is more robust by way of its design, being electromechanical, and is easily controlled with a mechanical or digital timer. This design is more tolerant (but not invincible) of dirty power, spikes, and surges. And they get along well with GFCI breakers (2014 National Electric Code requirement). And they are more efficient than their single speed cousins.
The VS pump offers infinite flexibility with its pump speeds and flow, but it comes at a premium. They cost more because of their construction and motor controller. They are electronically driven, the heart of the motor controller is something called a Variable Frequency Drive (VFD). VFD's are more delicate and a lot more sensitive to dirty power, spikes, surges, and lightning. They are also known to nuisance trip a GFCI breaker often, especially during startup. VFD's put out harmonics on the power wires, and this is the most common source of the nuisance GFCI trips. These pumps are the most efficient.
Other factors to take into consideration is:
-Your electric rate. Higher rates favor the use of VS pumps. A two speed will still be more efficient than a single speed.
-Pool setup. Larger pools, built in spas, and water features often require a larger pump and/or higher outputs to ensure adequate flow.
-Cost. VS pumps are more expensive than the 2 speed pumps. Some utilities will offer a rebate on a VS or a 2 speed (like errorz utility does), never hurts to ask.