I think most people would say black for watching videos. The black border will blend better. With that said, I have a white iPad 3 and have no issues with watching videos and I don't find the white border distracting.
I have both the black and white 4's. Honestly, it's just a matter of personal preference. Nothing scientific about it and if you poll 100 people, the answer you'll most likely get corresponds to the iPad color they've already purchased.
tbh, I think its really personal preference. I've seen people post that the white is better for videos and conversely the black. Get the one you like and is the least distracting.