If you're talking USA then yes a $100 price difference would give Xb one the win for the generation, I think. But that means always being $100 cheaper, which means if PS4 cuts to $299 Xb one needs to cut to $199.
Globally, $100 wouldn't cut it. Indeed I don't think there is a realistic price low enough that would cause Xb one to outsell PS4 world wide. And certainly not one that will make it eat up the current gap and pull ahead.
However if MS gave away the Xb one then they would be onto something. How can they give away Xb one?
Buy any 3 MS published games at full price (no revenue to 3rd parties) and get a free Xb one. OR
Buy any 4 MS published Xb one games at full price and a year of XBL gold and get free Xb one + Kinect.
Either or both of these deals for the lifetime of the Xb one. I would go and get an Xb one right now and buy FH2, Ori and the Blind Forest and Sunset Overdrive to score my free Xbox one.
Do it Microsoft, you know you can afford it. It will only cost you about $20Bn over the lifetime of the console, and you can make about 30% of that back with future game sales and live subscritions. So the net cost is only $14Bn. Everyone knows that's just chump change for you. Just think of the benefits that would come with having the top install base console for the generation.
“The fundamental cause of the trouble is that in the modern world the stupid are cocksure while the intelligent are full of doubt.” - Bertrand Russell
"When the power of love overcomes the love of power, the world will know peace."
Jimi Hendrix
