Hi Azomyr
You have asked a very good question, and probably the most important one if you want to learn both Japanese and PRC Chinese characters.
The following information are all from my personal effort as one of my goal is to pass Kanken 2.
There are 2136 Joyo kanji, which is the Kanken 2 level, out of the 2136, there are total of about 860 kanjis that are different from the PRC after simplification/modification by both nations.
This number include all the discrepancies including Wasei Kanji, and stroke difference,so if you consider kanjis like 反, 戸, 所 etc to be the same in both Japan and PRC, then the number will be smaller.