Synthetic oil has a different flow pattern, it may still be 5w-30 or 5w-whatever, but it is still thinner than conventional oil, Therefor on an older car, you may find leaks where there were none before, also your valve train might be a bit louder due to the thinner fluid, their is nothing wrong with using synthetic oil on an older car, it is not going to set it on fire, it's just something you can consider when thinking of changing to Synthetic oil, Most "synthetic" oils are actually a blend, Look for things like Castrol syntec, or Mobil 1 to find full synthetic written on the bottle.
I used to use Castrol High mileage Synthetic Blend, but recently I switched back to my old faithful Pennzoil High Mileage conventional, and my valve train is a bit quieter, and the sound of the engine is a bit smoother, And a pin hole drip I used to have, is not there anymore, So these are all just things to consider.
No performance gain that I can speak of, but some people swear more expensive oil gets them more horsepower.. But if I spent 9$ on a quart of oil, I would want to feel more power as well.