I have both....running Rival S 1.5 for national events and RE71Rs for locals. BFG has better contingencies(or in the case of ProSolo, only one with contingency) and I have a codriver than can win those, so BFG makes sense. I just been buying used RE71Rs for other events.
Driving wise, the BFGs feel much sloppier, there are more delays to your inputs and you need to lead the car more (turn in earlier) to get the car to work. They also have better tolerance to mistake, in that if you jam on the brake too late and turn in the car might still make it. Bridgestones are not very good with that. Bridgestones are much sharper and reactive to drive. I prefer their feel but I don't hate the BFGs, I hated the 1.0 version but the 1.5 is tolerable. I am curious to know if they will get better when I stick my custom front struts back on(they got sent back to ProParts for rebuild and will be reinstalling them this week).
Driving back to back earlier with the 2 tires I think their ultimate pace aren't that different. If you are fine with the BFG's characteristics I think either one will work. BFG obviously are pricier. They also wear faster on the shoulder than the RE71R, which makes it that much less appealing...