In my limited experience, there are two very different S&W DAO trigger feels.
1) The original 3rd Generation DAO guns with the extended (at the rear) slide.
2) The newer (including TSW) guns that use the standard slide.
The original guns partially cock the DAO hammer (think of a hammer-fired version of the Glock action or the HK LEM), so the trigger pull is shorter and not as heavy. The newer guns have a true DAO trigger (like a revolver) and the trigger finger fully cocks and releases the hammer. The newer action requires more work from the shooter and, to me, is like the HK LEM when in the uncocked (second-strike) mode. It is not a particularly nice trigger feel.
The older DAO action has better geometry from a leverage view, allowing for the shorter and smoother trigger pull. This is important for shooters with short fingers as the older guns have a shorter trigger reach. I have found that shooters, including me, who can shoot the older DAO guns very well often struggle with the trigger reach on the newer DAO guns. My personal belief is that the older DAO action was well ahead of its time, especially with today's emphasis on SIG's DAK and HK's LEM.
The older gun's action feels (to me) like a very nice revolver action. The pull is very smooth and not very long. It is longer than the Glock trigger, but is much smoother, lacking the annoying "sprong" break. It lends itself to a rolling trigger pull. The reset is noticeably longer than the SA reset on the S&W TDA. It really feels like the revolver's reset.
A functional difference is that the older DAO, like the Glock SFA, does not have a second-strike capability as the cycling of the slide is needed to pre-cock the hammer and put the action in position to move the hammer. If the hammer falls and the cartridge in the chamber does not go bang, a "tap-rack" immediate action is required to get the gun running. The newer DAO guns have a true second-strike capability, but my training has me do the "tap-rack" immediate action. That training, combined with the fact that modern ammo is very reliable, make this difference insignificant, especially when the advantages of the older DAO action are considered.