Eric is correct. The end user will not see much of a difference. However there a lot of technical differences. I will point out a few.

IGBT's have a lower on state voltage, this means that they run cooler, more power to the stick, less loses due to heat. efficency!

The large currents used in welding require parallel semi conductors. so anouther words they take ten 30 amp parts to get a 300 amp output. If for some reasion one part is less efficent and burns out at 25 amps then ALL the parts will fail at a 300 amp draw.
The welder will be dead.

With MOSFETs the circuts to prevent this problem is quite elaborate. The more circuitry the higher the possibily of a problem and a failure.

With IGBTs the solution is much easier, and requires much less circuitry

The IGBT is more efficent and better reliability.