Very similar. Have used them both. Cup 2s a little lighter, quieter, and maybe a bit more nimble due to their lightness. Re-71R probably a little grippier at their peak, heavier, and can feel like velcro when going over tar strips on a hot summer day....very sticky tires. I have gotten about ten days out of each tire and tend to heat cycle them out before destroying the tread. Need higher camber greater then 2 degrees to get the grip and make them last, otherwise you will prematurely wear out the outside edges of the treads.
Both great tires, but the Bridgestone's are much cheaper and probably a tic faster. You will be 1-2 seconds faster per lap with these tires as compared to normal street tires. The car will handle much better as expected, but you will also increase your grip under braking. I have seen 1.38 on the G meter which is way higher than street tires. You can go deeper into the corners and out brake anyone not on such tires. Happy hunting when you get your new shoes.