I've designed many of these constant pressure systems; I was designing them for community water systems and trailer parks and using VFD's (variable frequency drive) and custom controllers before Grundfos put out the package systems. I also did two massive system designs for golf courses, where we used VFD constant pressure pumping plants to feed valve in head, individually controllable sprinkler systems, and used water features on the course for water storage. I really enjoyed designing these type of systems.
The advantage to them is that you can have storage in a much more compact space than pneumatic bladder tanks, if you need the storage. Your well pump also pumps against a constant pressure instead of a variable pressure, so you can design it to pump more efficiently.
The constant pressure systems, ideally are pumping from a non-pressurized tank, through a small (usually less than 3 gallons) pressure tank, to the house. The small pressure tank is to avoid water hammer as the pump starts and stops, and to allow for a small amount of leakage (like a dripping faucet) or someone getting a glass of water to drink without the pump coming on. The pump is a variable speed pump, that varies how much it pumps to keep the pressure at a set value. It shuts off entirely when no water is being used.
The downside to a constant pressure pump is that it is a bit more complex, and costs a bit more. You have two pumps to buy (well and constant pressure booster), and a tank. The tank costs a bit less than a pneumatic tank, though. The benefits are:
You get more even pressure, and greater capacity for water use without running out (you can size the holding tank as big as you want).
The well pump is working against a lower, more standard pressure so it generally lasts longer and is more efficient.
You can store more water for irrigation and peak use, if your well can't keep up with that peak use.
Addendum: Reading your question again, you asked about a vfd to control the downhole pump. I see very little benefit to those, it puts the complex and expensive pump down the hole, where it is harder and more expensive to maintain. The only advantage I see to constant pressure systems is if you use a non-pressure storage tank, with a level control that runs the well pump instead of a pressure switch. I see very little benefit to using a VFD pump down the well, except possibly if you had essentially unlimited well capacity, so you use it as your "storage" to meet peak capacity. In that case, you'd be trading off more costly maintenance against having above ground storage.