I missed this thread as I was sick and in bed for well over a week (still am).
There are plusses and minusses for all the devices mentioned here. It becomes a matter of what you want for your type of shop stuff and budget.
For example... a VFD (variable frequency device) produces nice balanced 3-phase juice and can serve as a great speed controller. Electronic speed control on a lathe is a real treat. Limitation ???... VFD's are dedicated for one machine only. A single unit will not power up your 3-phase shop. The big HP VFD's tend to be rather spendy.
The "Phaso-matic Converter" device is simply a starter to launch an ordinary 3-phase motor and run it on single phase current. They will run one machine (at a time). I have used one on my Cincinatti mill for years as it was my only 3-phase machine back then. Drawbacks ???... You loose HP from your machine's original rating as it is receiving only two hot legs of juice not three. Some electric motors can't handle this but most can. Once started the device kicks out and the three-phase motor continues on its' merry way on single phase current.
Rotary phase converters use an idler motor to "chop up" the single phase current into three-phase. As stated they do this by acting as a motor-generator. The fancy commercial rotary phase converters have a starter circuit, auto restart circuit (in case of temp line outtage), and over-load protection. They also have caps that match-balance the voltage of the 3 out-put legs. The RPC unit can power up an entire shop as long as the device power rating isn't exceeded. Using one machine (load) at a time sidesteps these issues. RPC's are pretty durable too. Downside ??? The big HP commercial RPC's are expensive. Some CNC machinery is sensitive to any slight voltage variation (the processors rather than the drive motors).
Home-built RPC's can be cheap and as simple as a kick-start, rope start, or pony motor start idler motor (30% to 50%) larger than the largest machine on line. The home-builts can also be as fancy as the big buck commercial units if you are an electric enthusiast. We had a very fancy homebuilt RPC in my friend's large machine and fab shop. It was eventually replaced with 3-phase on line in the new industrial center shop. My friend kept this neet RPC though I tried to buy it from him for my new shop.
You really do get your nickels worth of juice from 3-phase which is why industry uses that type, stronger, cheaper, mo better !!!
The choice is yours (quote from my Brit Army recruiting T-towel of regimental crests).