Not only will there be simply vast performance gains, but even between Java 6 versions there are big differences. I tracked minor releases of Java 6 over an 18-month period and saw 15-20% speedup just from that.
Java 7 is out, by the way, and is the preferred production version - is there a reason why you wouldn't want to go to that version?
Oh, and one last thing. If you need to prove the gains to management, then you should read up a lot on performance measuring of Java applications. I have an article in the upcoming May / June 2012 issue of Oracle's Java magazine which is a real 101 if you need it. It's a very slippery subject, so you should do plenty of reading or you may get very misleading numbers.