In practical terms, VVI and CSI are old technology using slow output switching devices to convert DC back to AC.
Because of their slow switching, the best these drives could do is simulate a sine wave by producing a large step positive, then another large step positive on top of the first step, then stepping down to the first step and then going to zero. The negative part of the sine wave was simulated the same way only with the polarity reversed.
This crude sine wave caused the motor to be very noisy at low speeds and also limited the motor's ability to rotate smoothly and develop its proper torque. In fact, at very low speeds you could actually see the shaft cog from one position to the next in time with the six voltage steps.
When these drives were state-of-the-art they were used on fans and pumps quite successfully because there was no need for low speed performance but they were not usually suitable for industrial machine drives.
PWM has changed all that with drive/motor systems now able to produce smoooth rotation and full rated torque at speeds at or near zero. Using anything else today would be a mistake.
Looking back, there are only two things that come to mind that were better in the VVI/CSI days. You rarely had EMI/RFI problems with the motor leads and motor insulation was not stressed as much on inverter power.