Do gliders make a better pilot?
I may be biased because I learned in gliders, but, concerning how soaring biases students to be better "stick and rudder" pilots:


The obvious one that has been covered in the linked answer: gliders don't have an engine.  The result of this is that flying a glider is an exercise in energy management and a more direct interaction with your drag polar for a given configuration--because you don't have any way to add more energy to the equation.


In other words, your duration aloft, your ability to land in a particular location (of particular importance in a glider, since you only have 1 shot at landing and it could be unexpected due to variations in ridge lift, etc.) -- everything relies on flying the aircraft so as to manage the kinetic and potential energy of the aircraft to achieve a certain end -- and you don't have any "liquid" energy (e.g., fuel) to add to the vehicle.  Generally, you're trying to fly the aircraft such that it creates as little drag as possible, so turn coordination becomes more important (also can lead to spins, depending on condition), speed to fly for prevailing conditions and flight mode becomes really important.

The quintessential example of this (at least, the one that I have a video of) is from a student at my undergrad.  He was learning to fly one of the Grob 109b motorgliders the school owned.  As part of the class, the students demonstrated their skill at managing the aircraft's energy by starting, with the prop off, 1000' above ground and maybe 600' from the end of the runway (horizontal distance).  Within 15 seconds, the aircraft would be on the ground just a little way beyond the runway numbers.  And you have to do it without exceeding the aircraft's maneuvering speed during the vertical dive, conserving enough energy to make the runway, but not too much energy (else you'd just float the length of the runway).


Another facet of the above: increased adverse yaw effect.


In a glider, keeping the yaw string straight (e.g., maintaining coordinated flight) is constantly drilled into you as one of the most important things you will do (besides flying the airplane).  I remember flying one of my last instructional rides before my checkride and my instructor walked up with a sheet, taped it over what instruments the glider did have, and said, "Let's go flying".  The only instrument I could see was the yaw string, and the point was that that was "all" I needed (I had a feel for airspeed based on pitch).

What the yaw string does is tell you whether or not you are flying straight (i.e., what direction the relative wind is going relative to the aircraft).  As noted before, this is quite important, because, if the relative wind isn't parallel to the longitudinal axis of the aircraft, your drag is going up.  Gliders are, typically, more prone to slipping or skidding (i.e., flying at angles to the relative wind, particularly in turns) due to their long wings, which, when they have an aileron deflected, can induce a greater yawing moment than your typical general-purpose aircraft with a much lower aspect ratio wing (i.e., a more shorter, stubbier span, whereas gliders are made with long, skinny wings to decrease induced drag).  This makes the aircraft's yawing moment more sensitive to aileron deflections and  more prone to fly in an uncoordinated fashion--hence instructors make it a point to train glider pilots to pay more attention to how coordinated their vehicle is at a given point in time.  

This is of particular importance, not just for drag, but also for flight safety.  If you have a glider that's low, relatively slow, and making a steep turn while landing (read: flying at a high load factor, thus increasing stall speed), an uncoordinated turn can do this, or stall, spin, and crash due to insufficient altitude for a recovery.  It's a really big deal, and, again, you don't have the ability to just "add power" when you feel like you're getting slow.


Situational awareness


One trick with gliders is that you are very dependent on the atmosphere.  Say you are trying to get from point A to point B, say for a race or what have you, and you planned out your flight to run a ridge based on forecasted winds.  You're up, running the ridge at 200' (or less) above ground level, and the wind peters out and dies -- you're stuck.  When I learned to fly ridges, the mantra was to always have a place picked out such that, if the wind died right now, you'd have a place to land.  200' was relatively high among the folks I knew flying the ridge (most guys would be flying at least half that, and I heard stories about folks flying at 20 feet above the trees), and that doesn't give you a lot of time to figure out where you are going to land...and landing out (i.e., not at an airport) is not uncommon.  Glider pilots train for it, it's part of our ground school, and it's beat into us while flying.  If you're taking off via aerotow (i.e., being towed to altitude by another aircraft), the question during training is always, "If the rope breaks right NOW, where do you land?" Because you're getting energy from the towplane burning fuel on the other end of the rope, and, as soon as it's broken, you have not much time, some speed, and usually very little altitude to get safely to the ground in.

So, in the end, I'd think that glider pilots would have some edge in powered pilots in that regard.  Yes, powered pilots train for engine outs, but, in a glider, every flight is an engine out situation and you're flying at the mercy of the weather, how well you planned ahead for it, and how well you continue to plan while you're flying.  As quoted from an AOPA article:


  U.S. Air Force Capt. Danny Sorenson, who instructs in F-16s, is a glider pilot. He stated, “As a result of my glider training, I’m always thinking, ‘Where can I land this thing?’” He also noted that during his F-16 training, simulated flame-outs were never a problem for him, “It’s instinctive,” he said. “I’d just fly my pattern and glide in.”


Summing it up:

Gliders are much "simpler" flying: there's not a VOR in a glider, no ILS, no autopilot...all you have to do is fly the airplane, and do it well.  And, if you do it well, the airplane flies well.  Do it poorly and you might die (if it's that bad, since you don't have 2nd chances in important things, like landing) or you just might not be in the air for very long.  It's a much more direct connection between the pilot's stick/rudder inputs, the vehicle's performance as an aerodynamic vehicle, and how the pilot wants to use the aircraft, though, and I think that's the key...and all of these skills translate to other aircraft (even rotary wing, as I found out when flying those once).

Sources:

--My experience (PPL in gliders)

--https://www.aopa.org/news-and-media/all-news/2002/may/flight-training-magazine/gliding-your-way-to-a-pilot-certificate

-- https://www.aopa.org/news-and-media/all-news/2009/january/22/training-for-that-moment-when-every-second-counts