I've run synthetic in transmissions and have had exceptional luck with it. If the tranny uses gear oil or engine oil it's great. I've run in in automatic transmissions and have found it lacking so I switched back to regular ATF products. The synthetic was noisier.
Cosmo, I started using synthetics in race cars because I was having problems with oil temperature in a couple of applications. The synthetic could handle that better and when I went to Mobil 1 the temperature went down too. I have run many hours of dyno testing as I developed a couple of motors and I am absolutely convinced of the value. Simply you get more power with less wear and better cold starts. If you have a turbo it's even more important. If you have oil leaks you leak more so fix them first.