For handling on a perfect road surface there will not be much difference in how fast you can go through curves between and design IRS and a live axle suspension that is equally well designed.
Where the difference comes about is in the real world of imperfect road surfaces, bumps potholes, cracks in the pavement, transistion strips, etc. On a live axle, both rear wheels are tied together so whatever one wheel does effects the other wheel. When you're in a corner and one wheel goes over a bump, it causes the other wheel to move to which can make the car hop sideways. On the street it's usually just a discomfort. On a road race track it costs you speed.
In EVERY road racing series where IRS is allowed in the rules, IRS equipped cars dominate the races, no ifs ands or buts.
Drag racing is another story.
Back to your original question, the advantage of a good IRS on a street car is that the ride can be more comfortable and in hard cornering on imperfect roads the rear end will have less tendancy to side-step.
For road racing cars, the advantage of IRS is that you go faster.