The Lawman was a later design that was built with more "modern" manufacturing methods.
It used cheaper-to-make key parts (hammer, trigger, hand, etc.) requiring a lesser (or no) amount of hand fitting.
Can't be tuned quite like the DS.
Was the fixed-sight version of the Trooper MKIII action.
More durable action overall than the DS, but when something wears out it typically requires finding a new part that already fits, as opposed to a new part that's fitted individually in the DS.
Trigger could break around the pivot pin, like the full-sized version, but that wasn't common.
D should be along shortly to say the Trooper MKIII/Lawman frames themselves were quite strong.
Aside from that, you're comparing a .38 to a .357 Mag, as noted above.
There were two Colt Lawman models with two barrel lengths, 2 inches or 4 inches.
The Mark III version in 2 inches was first made with an exposed ejector rod like the 4 inch version, then in later production was changed to a shrouded barrel with the 4 inch keeping the exposed ejector rod.
The Lawman Mark V was also available in 2 or 4 inch barrel, with the 2 inch having the shrouded barrel.
The Detective Special is a small frame revolver, the Lawman was a heavy medium frame revolver with a much larger diameter cylinder, and is a rather significantly larger, heavier revolver.
The DS was a design dating back to the 1890's with a hammer mounted firing pin, the Lawman a modern transfer bar-safety-ignition system design.
The Detective Special in the later years was rated for use with "up to" 3000 rounds of +P ammo.
The Lawman was rated for unlimited use with full charge .357 Magnum ammo.
There are significantly more holsters, grips, and accessories available for the Detective Special.
There are few holsters or grips available for the Lawman, especially in the 2 inch versions.