Let me break this down for you as "newbie" as I can, as I don't know your firearms knowledge, training, or expertise levels. So please bear with me.
Obviously you know what SRT stands for Short Reset Trigger. SIG developed the SRT system to shorten the reset of handguns they make increasing accuracy, follow up shot times, and consistency.
So how does it work, it simply shortens the rest of the trigger, if you are curious you can do the following.
To see what your current pistols reset is as long as its not a 1911 pistol thats of high quality do the following:
1. Clear the gun, make sure there is no round in the camber, or a magazine in the gun.
2. Operate your slide to allow the gun to dry fire.
3. Pull the trigger and HOLD the trigger to the rear.
4. While holding the trigger to the rear, recock the gun.
5. after the gun as been recocked slowly release the trigger until you hear a click and the trigger "thrust" forward.
When the firearm clicks and the trigger "thrusts" forward that is the point of trigger reset on your firearm, the point of reset is wear the trigger can be immediately pulled again.
So based on where your reset is can effect many things, like groupings and how fast and accurately you can make a follow up shot(s). The farther your trigger has to go forward the more "play" you will have in hand position, point of impact, and overall operation.
With an SRT trigger the reset is what i can consider about 60% shorter than a standard firearm. If you own a high quality 1911 the reset is very close to or the same as your 1911, as 1911's usually come standard with a shorter reset trigger. And while most SIG platforms are based around a 1911 style frame/grip it mimics the use of a 1911.
To answer a few of your other questions: there is no down side to an SRT system, the less reset, and the faster you adapt to the trigger the faster you will have more consistent groups and follow up shots. The DAK trigger is a double action only pistol that is used by a few groups of the Government, while other groups use Sigs with SRT systems, its all based on what that agency whats there employees to carry.
A DAK trigger is no comparison to a SRT setup.
The only reason to stay away from a SRT is if you don't want to relearn shooting with this style, meaning you grew up on revolvers, mostly own and shoot revolvers.
I 100% recommend an SRT trigger system. But sometimes you have to experience it to understand. Do know you can add the SRT trigger to any DA/SA trigger system SIG for $80 in parts do it yourself or I think SIG charges 95-105$ to do the work including parts, but there turn around time is 3-4 weeks right now.
Good luck and happy shooting.