MS knew Sony had a stronger GPU but they didn't care because they figured they would rule with multimedia features due to their 8 GB of RAM. Also it would have a huge advantage in a lot of games due to the much greater RAM space.
They figured the PS4 would have big bottlenecks with only 4GB of GDDR5 RAM and it was a mistake for Sony to use such expensive RAM. X1 would have 8GB of RAM and 5 GB for gaming and 3GB for OS and multimedia device. Sony they thought would be 3GB for gaming and 1 GB OS and multimedia. It would have a gimped multimedia interface that could never catch up to X1 all because they concentrated on gaming and even then it's still hampered with 3GB of RAM vs 5GB for X1.
Then Sony announced 8 GB GDDR5 RAM and holy f*ck what a sneak move, MS is still reeling from that. They really never had an answer for it and now they just have a more expensive system that they have to just try to buy their way into the market with investing in exclusives. They thought this gen would be easy.
It worked out well because I like competition and if Sony didn't do well with PS4, it would be their last console. Anyway, 8GB GDDR5 RAM is what layed the smack down on MS, not the GPU in of itself.