Sorry, couldn't vote on your poll because I prefer neither as a first choice.
I prefer TDA (DA/SA). Too many years training and carrying issued and personally owned TDA pistols. Many more (previous) years of shooting both DA revolvers and SA 1911 pistols developed my DA & SA trigger skills, and then I discovered I preferred the TDA's DA-SA transition. Not everyone thinks similarly, though.
I prefer the SA trigger for deliberate, precise shots. I prefer the initial DA trigger stroke for general defensive purpose, but then I spent several years carrying S&W DA revolvers as issued weapons.
I dislike the feel of the LEM trigger.
I know a LEM user who experienced some trouble trying to qualify on a rather standard bullseye course of fire, and was able to do much better when he borrowed a TDA pistol.
Different strokes (literally
) for different folks.
If I HAD to choose from the two designs listed, it would have to be the DAK ... but I place the DAK as a distant second choice to a good TDA.
The primary trigger stroke of the Enhanced Double Action Only (DAK) requires approx. 6.6 pounds of pressure to fire the trigger, and it's the 'full length' trigger stroke of the two ...
The intermediate trigger stroke requires a partial reset of the trigger, and a heavier (approx 8.3 pounds) amount of pressure to fire the pistol.
Granted, the primary trigger stroke actually tends to 'feel' lighter to many folks, because of the excellent geometry of the design ... but it's long, too.
When I asked an armorer instructor during my Sig Sauer armorer's class why the shorter reset trigger stroke had to be heavier ... since that's not generally the way of it in TDA pistols ... the answer given was that it was Sig's determination that it was 'safer' to have the shorter trigger stroke require more effort on the part of the user/shooter.
Remember, even though these pistols are sold in the commercial market, much of their intended market is military & LE contracts. Safety is a marketable attribute.
I've seen cops (and some non-LE) experience ND's on a range when they had their fingers on their triggers, but weren't desiring to intentionally fire a round. I've seen it occur with SA, TDA & DAO-type pistols. The significant number I can remember offhand involved either cocked (SA), or DAO-type triggers which had only been released to shorter 'reset' positions ... although I can think of at least one where a heavy DAO trigger was fully stroked by the owner/user by 'mistake' (negligence). "Finger off the trigger unless you're intending to shoot" and "Watch your muzzle" are a couple of my well-used comments on the firing line ...
Given my druthers, I tend to prefer the heavier initial DA trigger stroke of a TDA trigger, and can certainly see why Sig Sauer supposedly intentionally designed the shorter, intermediate reset of the DAK trigger to be heavier. Safety issues.
Regardless of how the gun is designed, though, safety starts between the ears ... and ultimately rests there. User error and mistakes aren't the fault of the tool. I've always enjoyed attending other folk's training where safety was paramount, and trigger/muzzle safety was consistently monitored. People can do strange, unexpected and unintentional things during moments of stress ...
Just don't mistake my personal disfavor of the LEM & DAK designs, or my reluctant "if I had to use one" choice of the DAK as anything other than personal choice and opinion, however. Both manufacturers produce excellent products, and there are satisfied users/owners of both found easily enough ...