I am flying an AnyCopter with a MultiWii and am dealing with the same issue. I was running 1450 kv Suppos with 8045s and got it to fly pretty well. I swapped out my Suppos for 1000kv Maytechs and 1045 CF reinforced rotors and the PIDs were WAYYYY off. I wobbled into the plants and it was just ugly.
I have had to reload default settings and, in between snow showers, am working on level flight without the toilet bowl wobble. I was able to tune it to the point I may make short flights with brief stops to let the sensors level. At this point, I need to rebalance motors and rotors to keep fine tuning.
Once I paint two rotors yellow, I will balance them and the new motors and the mount a GoPro. I am changing motors, rotor size and rigidity and adding 210 grams.
Every change will require some type of PID tuning to make it fly right. I figure I am practicing how to tune the MultiWii at this point.
https://www.youtube.com/watch?v=HAAw5fdHmcU