Advantages of 19" wheels:
- All things being equal, they are more efficient than 21" wheels
- They have more sidewall to cushion the rims against potholes and other road hazards, so are by far the better choice for poor road conditions
- The wheels themselves and tires are cheaper
- An argument can be made that they confer better performance/acceleration because of decreased unsprung mass
- Generally quieter
Advantages of 21" wheels:
- Appearance
- Appearance
- Appearance pretty much only
- An argument can be made that they confer better handling characteristics (exclusively in racing/high-performance driving) because of decreased aspect ratio/sidewall and less sidewall flex
at the extremes of traction encountered only by high-level racing/autocross
- Generally much better selection of ultra high performance or racing tires for the Model S total wheel/tire diameter (not specific to 21" wheels, just to 21" wheels on the Model S specifically)
Staggered wheels:
- Theoretical increased traction on the higher-torque rear motor in performance Model S due to larger contact patch
- Has repeatedly not been proven to make a difference in 0-60 or 1/2 mile times with P100D
- Rear wheels have greater mass
- Not able to rotate tires
- Arachnids are only offered new from Tesla in staggered (many anecdotes of people swapping the rear 9" wide Arachnids for matching 8.5" wheels for a "square" setup of 4 identical Arachnids... I'm thinking about doing this with mine)
The main reason that 21" wheels are less efficient than 19" is because of increased unsprung weight with the 21s - just more mass to move and more rotational inertia to pour energy into moving. This can be mostly overcome if you get 21" wheels that are lighter - for example, expensive forged 21s will be lighter and more efficient than cheaper, heavy, cast 19s. The contact patch of the tires is only a minimal factor as it's minimally different between 19s and 21s. Of course, even though Tesla doesn't offer lightweight 19" wheels, multiple expensive aftermarket forged options available which would be lighter than any 21.
I agree with
@Ostrichsak that the TSportline 19 inch wheels look great and negate most of the benefit of getting 21s (appearance: those turbines and arachnids are HOTT!). I would recommend to most people to just go with 19s, always. I have 21s with stickier tires and smaller sidewall only for the summer to autocross my whale of a Model S.
I also agree with
@beatle that MXM4s on 19" Cyclones yield a pretty good ride even on a Plus suspension. There, N = 2.