The style of MOSFET chips used in this Fulltone Fulldrive are more commonly found in tube amps of the 80's and late 70's. So I'm guessing it's just a vintage reissue pedal.
MOSFET stands for metal-oxide-semiconductor field-effect transistor... These transistors have largely been replaced by the CMOS versions which are an upgraded version of the MOSFET circuitry... Hard to explain it all in general terms without going into a long drawn out history lesson and electrical engineering 101 class....
In short, The MOSFET system was probably the circuitry that was first featured in the original Fulltone Fulldrive pedals back in the 90's... My guess is that this offers a bit more warmth but may also offer less tonal versatility... The newer Fulltone Fulldrive probably uses CMOS circuitry that utilizes multiple styles of smaller MOSFET circuits..... It will give you more tonal versatility but may not give you the solid vintage tone of the MOSFET exclusive version... It appears that the MOSFET version gives you the option of using the original MOSFET settings and the newer settings... So I would say go for the MOSFET version.... unless you're not that into vintage tones... Then just go with the cheaper Fulldrive without the MOSFET...
Hope that was helpful.