The M880 drivetrain doesn't look as beefy as the M1008 because its not. A M880 is a civvy 3/4 ton dressed up as a 1 1/4 ton, vs the M1008 being a civvy 1 ton dressed up as a 1 1/4 ton. Conversely, the M37 is a 1 ton downrated to a 3/4 ton offroad.
Dodge used a NP203 transfer case in the M880. Think of it operating like a open differential most of the time, but it can be locked. If you loose traction with one tire without it locked, only that one tire will spin (one wheel drive). With the transfer case in loc, one front and one rear has to loose traction to stop you (two wheel drive).
With the rear locking differential the M1008 has, with the transfer case in 2-hi both rear tires have to spin for you to be stopped (two wheel drive). In 4-wheel drive (hi or lo) both rear wheels and one front wheel have to loose traction (three wheel drive). For the M1008 variants with the front limited slip you have to have both rear tires and one front tire loose traction, plus overcome the friction provided by the limited slip (3.5 wheel drive).
As to your original question, I've used both a M37 and a M1008 as daily drivers over the years. The M37 looks better and is incredibly simple and reliable, but is noisy and slow. It will go almost anywhere. The M1008 goes faster, has better brakes and is more fuel efficient, but is longer, has less ground clearance, worse departure angle, etc, etc.
At the end of the day, everything is a compromise. The M37 compromised on-road abilities for off-road; the M1008 is the opposite. Modifications can be made to both to overcome their weak spots, so it really all comes down to personal preference.
Dodge used a NP203 transfer case in the M880. Think of it operating like a open differential most of the time, but it can be locked. If you loose traction with one tire without it locked, only that one tire will spin (one wheel drive). With the transfer case in loc, one front and one rear has to loose traction to stop you (two wheel drive).
With the rear locking differential the M1008 has, with the transfer case in 2-hi both rear tires have to spin for you to be stopped (two wheel drive). In 4-wheel drive (hi or lo) both rear wheels and one front wheel have to loose traction (three wheel drive). For the M1008 variants with the front limited slip you have to have both rear tires and one front tire loose traction, plus overcome the friction provided by the limited slip (3.5 wheel drive).
As to your original question, I've used both a M37 and a M1008 as daily drivers over the years. The M37 looks better and is incredibly simple and reliable, but is noisy and slow. It will go almost anywhere. The M1008 goes faster, has better brakes and is more fuel efficient, but is longer, has less ground clearance, worse departure angle, etc, etc.
At the end of the day, everything is a compromise. The M37 compromised on-road abilities for off-road; the M1008 is the opposite. Modifications can be made to both to overcome their weak spots, so it really all comes down to personal preference.