I have used all three systems, Static, Rotary and VFD. Each has its pros and cons.
I ran my South Bend H10 off a Static for years, never had a lack of power despite it only having a ¾ HP motor, meaning I was only really getting ½ HP. It came with the lathe so no additional cost and one could be easily made for about $20. However, it didn't run as smoothly as it now does off the rotary. Also, there was alway an annoying hum from the static converter.
I built my own Rotary converter out of a 7.5 HP motor, a few capacitors and relays. It works perfectly, the machines run smooth and deliver full power. It currently powers 2 lathes and a washing machine though I plan to add a drill press and switch over my compressor, when I have the time. I suppose the only cons are the sound of the idler motor running in the background (Though it is not at all objectionable to me) and the added expense.
My Mill, a Drill Press and Air Compressor run of VFD's. They offer the most control over the motor as that is what they are designed to do. You get, speed control, soft start, braking, overload protection, torque limiting and other features. Phase conversion is only 1 feature of VFD and often not even used. Many industrial machines use VFDs even though they are supplied with real 3 phase power.
The cons are the expense and the need to rewire the machine.
So the right choice is what works best for your machines, needs and budget.