From my understanding, there are multiple advantages that this system proposes.
1. On demand carbon availability: As opposed to vodka dosing, where you need to tailor the amount you dose to the level of N and P in your tank, the bacteria will simply subsist on the pellets and be limited by the surface area and the available N and P. Theoretically, the benefit is that you don't need to be as careful about the amount you put in a tank. Also, you don't need to be there everyday dosing carbon and worry about missing a dosage.
2. Carbon release localized to surface of pellets: Instead of releasing carbon in the water column, where it could be taken up by anything that might use it, the carbon stays with the bacteria that colonizes on the surface of the pellets. The advantage of this is that you potentially avoid those slimy cyano films that many people, including myself, have observed with dosing vodka or other carbon.
3. Bacterial mass and biofilm buildup localized on pellets - Yet another advantage to a localized carbon source. For those who have dosed a lot of carbon in their systems, I'm sure you're familiar with how much bacterial biofilm can build up on your rocks and walls of your tank. The benefit of a localized carbon source is that you can potentially keep the slimy stuff with the pellets and not all over the tank.
4. Optimizing removal of excess bacteria via skimmer: By having the bacterial growth on the pellets in a reactor that is placed right next to a skimmer, you can potentially make the removal of excess bacteria more efficient. As the bacteria sloughs off the pellets in the reactor, it can be immediately sucked into the skimmer and removed. This is opposed the typical scenario with regular carbon dosing, in which the bacteria grows on all surfaces and may not be efficiently removed, especially from areas of low flow.