Below is a great video of 13-year tennis pro Michael Russell being tested to see if he can pick his racket out of a bunch of very similar rackets. In one case he could tell a 1 gram difference in the weight of a test racket compared to his personal racket. Everything else – model, string tension, etc.- was similar.
For someone who plays regularly I'm a weirdly unpicky player when it comes to things like strings. Most players know exactly what kind of string they want, but I care mostly about tension. I've come across a couple of strings that I don't like but for the most part I don't pay much attention. 99% of regular players do care very much, but I've never felt my game was fine tuned enough for it to make much of a difference.
BTW, I had the chance to see Russell play in the qualifying rounds of the Winston-Salem Open two weeks ago and it was amazing to see how much steadier he was than his opponent. The guy is a hitting machine, and I was very pleased to see him put on a great show versus Andy Roddick earlier this week in a night match in Ashe Stadium at the US Open.
Anyway, enjoy the video.