I've owned my '77 1742 since 1983 and have several thousand hours of operation in that time. I can honestly say that I've only been "stuck" - needing digging or pulling to get me out - twice in that time. Both times I had driven down a steep incline off of a pile of snow and proceeded to bury the front tracks under a hard drift. Because of the steep incline, I was unable to back up and so had to dig. I routinely cross 30+ degree side slopes and routinely climb 30+ degree hard snow hills.
My Tucker has a 440 Chrysler gas motor and a NPG 5-speed manual. I've driven several diesel-powered Tuckers, one with a Perkins and an Allison auto and two with 4-53 Detroits and Allisons and none of those had the "punch" that the gas motor has - You're idling along and you punch the throttle on the diesels and they go harder but not in the same way the gas one leaps forward. The diesels also weigh a bit more than a comparable gas model in my experience because, especially with the Detroits, they motors are considerably heavier.
My 440 burns about 5 gallons an hour, so I can go about 10 hours on a tank.
My 1742 will easily climb up and over a vertical 4 foot wall of snow that would quickly stop a two track cat - the front tracks rear back and climb over while the rear ones stay firmly planted, driving hard. Once the fronts are up on the flat the rears rear back and follow.