How does a soft-start autotransformer compare to a regular autotransformer?
Normally "soft-start" style circuits are used for motors connected to equipment to limit the startup torque and reduce damage to equipment.

Other equipment can use this concept if large inrush currents would be damaging to the circuits or equipment.

Resistive heating elements like those used in cooking equipment would not need a soft start. Appliances should already have a proper filter circuit for their electronic controls to limit the effect of small voltage fluctuations or spikes. 

I can't really see the advantage to a soft-start for a transformer for appliances. If a product can handle being plugged in to 120 volts here in the US then they should certainly be able to handle it in Europe.

Good luck!