Does a higher speed rating mean faster times and more grip? Will a Y-Speed Rated (186 MPH) tire be faster and grippier then a W-Speed Rated (168 MPH) tire?
Not necessarily. Grip and performance depend on the tire's compound, bead construction and other attributes.
A higher speed rating means the tire will deflect less at higher speeds due to the tire's circumferential reinforcement, but the tire's compound may not be grippy.
Consider the tire results of Car and Driver's comparison test from last summer.
In the dry autocross test, the fastest tire was the W-Speed Rated Kumho Ecsta XS.