Soft starter VS variable speed drive

A soft starter is a basic device which will ramp up the speed of your motor to full speed over a preset time, easing mechanical stress and also easing the high inrush currents which can be experienced by starting a motor under load. A breaker will cut the supply to your motor if the load is too high. A variable speed drive will allow you to control a motor (to varying degrees of accuracy depending on the model selected) by varying the phase angle (amongst other things). It will give you the most control over your motor including at the most basic ramp time running speed.

Soft starters are also a limited time duty: the time that it takes to accelerate the load plus a few seconds. (the load takes 10 seconds to accelerate, and add a few more to that for insurance to compensate for different loads or lower power system capability). This limit on operating time makes them less costly.

Adjustable Speed Drives (ASDs, or VFD if you must) are continuous duty, full load capable forever. And they are quite a bit more expensive.
In some situations a soft start may not be possible, and a variable speed drive is the remaining best solution.

I have come across applications where a soft start situation would take two to three minutes. The typical 15 second drive wouldn't work. Another one that didn't work was on a 13.8 kV power system.
One of which is price. A VFD is considerably more costly than a RVSS- Soft Starter. If you need to control the actual time a motor comes to speed then you almost always require a VFD as a soft start controls phase angle of the voltage feeding the motor which limits the current to the motor. That gives no absolute about the ramping time unless the load never changes and the supply voltage is always constant.

Another thing to consider is complexity of the circuitry; while a VFD can typically offer many more auxiliary functions besides its ability to control frequency and ramp time it is much more complex in terms of design. Most utilize IGBT technology whereas most RVSS use Thyristors or SCRs.

I would also like to correct one thing most VFDs can operate motors above base speed (50/60 Hz.) some can operate at 400+ Hz. Realize of course you need a machine designed to handle those speeds.