Danielle,
One of the reasons for the lack of response here is that your question is ‘twisted.’ I doubt that you really want to know the difference between Primavera version 6 and version 3. You want to know the difference between P6, Version 6 and P3, Version 3.1. P6 and P3 are two different software products. P3 has never been an earlier version of what we now call P6.
P3 is a 16-bit software that was first released in 1984, was last updated to Version 3.1 in 2001, has been on restricted sale these past two years, and will be completely abandoned by Primavera at the end of this year. What we now call P6 was introduced by Primavera in 1998, has gone through at least 6 name changes, was at version 3 in 2002 and is currently called P6 (and is at Version 7 right now.)
Look around this site and you will see at least a half-dozen different postings on the differences between P3 and P5 (which is P6, Version 5) and P6. Good luck!