I've also experienced problems with the vertical navigation logic (hereafter called VNAV) with the Pro series, having bought the family bundle about a week ago. Interestingly, I haven't seen any particularly abnormal climb performances, but the descent profile certainly needs a complete overhaul. I'm still enjoying the aircraft, because while awaiting a fix from Aerosoft, I use selected descent with VS which thanks to my many thousands of hours on different sim platforms (FSX, FSW, X-Plane and P3D) makes me hit the FAP/FAF every time.
I think the VNAV descent sets itself up for trouble mainly because it calculates the T/D wrong, too hot (close) to the airport/runway. My experience with the A3XX Pro is around 100-110 NM from RWY, which is too little and leads to vertical speeds in excess of 3,000 feet per minute. From a passenger comfort and safety point of view, it's unwise to chase aggressive descent profiles (> 3000 fpm for longer periods of time). In addition to getting too close to RWY, the aircraft also goes into panic mode when flying certain segments of a STAR, eg. the RIPAM 4M for RWY 19R at ENGM. This STAR has waypoints with ALT constraints 9000A. When flying the 320, I was at the GM432 at 9,000, then the aircraft panicked because the next WPT was BAVAD 5,000A, 9 NM away, resulting in a dive-descent at close to 6,000 fpm, an overshot (or undershot?) of the altitude, resulting in the aircraft starting to climb again in order to reach 5,000...
Generally speaking, and in my opinion (formed by flying a huge fleet of various aircraft), not many devs can write the code necessary for a fully realistic VNAV logic, and often it's the descent profile that seems to be the most difficult to get right. I will refrain from giving any examples, but they are prominent devs... My purpose with this post is to be constructive and to help Aerosoft, a fantastic developer/publisher, so you can solve this little problem once and for all. You've already got the most stunning sim creation of an Airbus I've ever seen, both exterior and interior with industry-leading 3D modelling and texturing. My advice for the vertical descent logic is as follows: Have the T/D 130-160 NM out, calculating vertical speeds between 100 and 3,000 fpm, with up to 4,000 possible (add drag visible on PFD) for a short period of time with airbrake deployed to regain profile in situations with strong tail wind component. Look at which constraints are more important than others, and don't forget to calculate/include time for the 10,000/250 overall constraint (and yes, the real aircraft will try to fix this on its own, pitching the nose up to shed speed). Have the aircraft at FAF altitude (ready for GS interception, as dialled in by the pilot) a couple of miles before rather than after the actual point.
Lastly, and once again in my opinion, the banking speed of the aircraft is a little too fast and abrupt. It needs to bank more slowly, adding to realism and immersion. And yes, banking more slowly means starting the turn a little earlier, both in and out of the arc.