"Will factors like wear, noise level and traction differ?"
Maybe, but you should be able to determine the effect by looking at the UTQG ratings.
BTW, the noise level is more a function of the tread pattern, so in theory, the same size, etc., that should be the same between speed rating differences.
"....what in the tire construction differ?"
Basically, whether there are cap plies or not. The following is an extremely simplisitc overview:
S rated tires generally don't have any, T rated tires generally have cap strips over the belt edges, H rated tires have a full cap ply, V and higher rated have 2 cap plies.
There are lots of variations on this.
I can see where a guy with a 4 door sedan might question the use of a V rated tires - and I tend to agree. However, I personally don't recommend anyone use lower than an H rated tire on anything! (unless it's unavailable in the size needed.)
The short explanation for this is:
Adding a cap ply to a tire seems to disproportionally improve the tire's resistance to tire failure. Pretty much all tire failures occur in S and T rated tires (H and higher are almost immune).