The camera's both shoot 4k resolution. The largest difference is that the Phantom 4 can film at 1080P 120 fps which means you can create footage you can turn into buttery smooth slow motion. The Phantom 3 can film at 1080p 60fps which is decent for slow mo. Personally I don't film slow-motion with my Phantom yet.
There is a large price gap between the Phantom 4 and the Phantom 3 Pro. I would watch the video and decide whether and understand exactly what you are getting for that extra $400 US and whether it is important to you. The Phantom 3 advanced is almost similar to the Phantom 3 pro except it doesn't film at 4k. It is about $600 US less than the Phantom 4. If you don't need the 4k than that Phantom 3 advanced is a great buy right now for an excellent HD filming machine.
This is a new feature just on the Phantom 4 where the front camera's will sense if there is an obstacle in front of it and avoid it. This is a nice feature, but the these sensors are not available on the side, back, and top where the drone is also likely to hit an object. If you focus on developing basic flying skills and don't fly recklessly you don't need this feature.
I usually fly my Phantom 3 Pro within the 4 m/s - 8 m/s speed range to film footage even though it can go up to 16 m/s. Although the Phantom 4 can fly at 20 m/s in sports mode I can't see this being practical for filming, but perhaps if you want to fly faster than your Phantom friend this feature is for you.
There are other differences to discuss that you can see in the video.
I pull out all the stops in Phuket Thailand using a lot of automated flight to get footage of this beach paradise.
Singapore's looks like a futuristic city with it's Marina Bay Sands hotel and Super Tree Grove Garden. See it from above.
I brave the cold of the Vancouver Winter to bring you footage of downtown Vancouver to the snow capped mountains of Whistler.
The Phantom 3 Drone is not for everyone. Some people always want the latest toy.