The internal shaping in the cage is slightly different to improve upshift in combination with 2015+ chainrings and the 2015+ cage is also slightly narrower to better control the chain on downshift.
The reason for the new lever is two-fold - it's designed, by having a higher clutch release tension and different internal cable bushing design to prevent the problem that you have seen of the chain dropping big ring to small on occasion whilst allowing for easier upshift with the long actuator arm, and the "bar" that has been designed in to prevent more than a "two click" sweep on the thumb lever is there to improve the shifting under load on compact-style cranksets, reducing the risk of the chain falling to the inside.
Hence the recommendation to use a 2015+ ever with a 2015+ FD and the reason to keep making the older-design FD and levers / lever bodies ...