TIRES CONTINUED:
Two examples.
#1 While turning a corner the front wheels begin to slide and the car wants to go straight ahead instead of turning. This is known as understeer.
#2 While turning a corner the rear wheels begin to slide and the car wants to spin out. This is known as oversteer.
In either case you need to reduce the workload on the end of the car that is beginning to slide.
NOW THE TRACTION CIRCLE
The traction circle is nothing more than a graph of a tire's performance on a horizontal plane (in this case the road) in four directions, right, left, forward and reverse. The limits of the circle (depending upon the tire it may not be a true circle) define the tire's available traction in any given direction. So if your particular tire can generate 1G (as an example that closely matches the Z on OEM tires at normal load on good, dry, level pavement at about 70F temperature) in any direction, that, then defines the limit of this particular tire's performance.
TIRES CONTINUED: Traction, grip, adhesion, it's all the same thing and it is the key. I'll try to keep this basic. Every tire has it's own unique performance profile. High performance tires are optimized for a relatively narrow range of operating temperatures and loads (weight), reduce or exceed these optimum ranges and traction suffers to varying degrees.
WHAT THIS MEANS: If a given tire or tires lose traction, we (the driver) need to immediately identify the cause and apply the needed remedy to restore sufficient traction to allow us (the driver) the control needed to continue safely down the road.
No simple answer because your driving response is dictated by a whole bunch of seemingly contradictory conditions all playing out simultaneously in four directions at maybe sixty miles per hour with cars and guard rails and trees and cliffs all around you.
Based on my experience, it's up to you to decide if it works for you, I make no warranties:
IT'S ALL ABOUT THE TIRES: The suspension, the chassis, the aerodynamics, it's all about providing the tires the optimum environment to respond to the driver's commands. Here's why I can't give you a single answer to your question, tires are elastic and generally do not respond to the driving experience in a linear manner.
I'm limited to a 1000 characters in these posts so let me ask you this, other than regular every day driving have you had any track experience? Have you done any reading on vehicle dynamics, tire design and dynamics (including the "traction circle"), race car set up, suspension tuning, high performance driving or aerodynamics pertaining to vehicles operating on a ground plane? If the answer is generally or completely no, we will need to start at the beginning, so to save time please get me up to speed on your automotive (books, performance driving schools and so forth) and educational (any physics, engineering or technical classes) background.
The answer to your question is (the envelope please!), it depends on a whole bunch of variables. Indirectly you are asking why one racing driver is faster than another and the answer to that question is rarely simple because if it was we would all be champion racing drivers. Let me get back to you on this.
My opinion: VDC is your friend and should be on in normal driving, especially for rain, snow, ice or emergency situations. Turning the VDC off allows the car to be operated in the extreme fringe of the car's performance envelope (essentially, track driving or a similar situation) without the VDC second guessing the driver. The overpowering need to turn off the VDC for everyday driving is probably the result of a common hormonal condition frequently experienced by males of a certain age.
The DW is a dry/wet (a three season or Summer) tire. The DWS is a dry/wet/snow tire, commonly called an All Season tire. All season tires have a rubber compound that is less sensitive to cold temperatures, so as temperatures fall below 40F degrees the DWS provides increasingly superior traction compared to the DW. To make the most of this compound the designers add sipes (cut lines) to the tread to improve snow traction. So the answer is yes, the DWS has a compound and tread pattern that provides superior traction in cold and snow but at some sacrifice in traction and steering response in the other three seasons of the year. If you need to drive a Z in cold and snow the DWS is a smart choice but if you have no need to drive your Z in snow and cold the DW should be your first and only choice.
I had a one semester photography class in the early-mid 70's when I was considering going back to school to get a teaching credential in industrial arts (my BA was in history), that's my story and I'm sticking to it.
The wiggle you mentioned will probably diminish or go away altogether after the tires are heat cycled a dozen or so times. The rubber in a new tire is still quite chemically active, your new tires won't really show up for work until you've driven them at least 20-30 miles several times.
You've just discovered why most sports cars come with summer tires. The larger tread blocks reduce tread squirm allowing the tire to be more "precise". All season tires have a rubber compound that is more tolerant of freezing temperatures and a tread pattern that features many sipes (cut lines) for improved snow traction. The side effect is a slight loss of handling precision. As the tread wears the shorter stiffer tread will provide sharper more precise steering.
I loath all season tires and rarely buy them. Of course we don't have snow, ya gotta do what ya gotta do.