Do you have tracking protection enabled in IE? If so, temporarily turn it off (usually via clicking a blue circle with a slash through it in the address bar), and see if that fixes it. I've noticed that some websites don't load video until you turn off tracking protection. I can only imagine that Google Chrome has less stringent protections against tracking because their entire business model is centered around tracking web activity.
So I tested few more 1080p YouTube videos and checked the bandwidth used by right clicking and choosing "stats for nerds".
What's interesting is that the bandwidth used was between 2-2.5 mbps and there was significant delay due to constant buffering.
I also checked my internet speed and it's pretty consistent at 5 mbps. So the question is, why is the YouTube 1080p video only using 2-2.5 mbps and not the full 5 mbps?
I did try turning off tracking and that did not help.
I'm not sure your ISP has the capability to selectively throttle when you use IE vs. Chrome, and I can't see why they would care what browser you use. It would be interesting to see the bandwidth you get using Chrome to access YouTube. If it's higher, it raises some interesting questions about the source of the problem as the data rate is a function of your ISP and the sender. I have a feeling the sender cares a lot more about people using IE over Chrome than your ISP.
I just played the same 1080p video side by side using chrome and IE desktop.
What's strange is that the used bandwidth was about same for both browsers. However, chrome plays the video a lot more smoothly with very few buffering while IE was constantly buffering.
I took screenshot of the video stats and noticed the browsers were using different Mime Type and "codec". I'm not sure if that's the reason for the performance difference?
It doesn't matter if you use any codecs, Chrome or IE. Clearly it's OP's ISP as YouTube MetroIE on my Surface Pro 3 i5 256 uses almost all of my 100 Mbps Bandwidth for 4K video playback via WiFi.
FYI, 5 Mbps can barely play 1080p without buffering. If you can get another ISP that can offer at least 10 Mbps, you won't be having any issues at all. For 4K, you need at least 45 Mbps to have no buffering.