You are pretty close to the max throughput of your Xbox. A regular category 5 ethernet cable will carry that data throughput.
Category 5e will carry gigabit.
Category 6 will carry gigabit and 10 gigabit (10 gig for distances under 58 meters).
Most current game consoles that I am aware of that have networking features, use either a 10/100 ethernet adapter, OR a WiFi connection. (My Wii uses 802.11n 150mb/s which rarely gets near that #).
I am assuming your internet connection speed is 150 mb/s and not your ethernet. 150 mb/s is not a standard ethernet speed rating. Odds are you are running something along the lines of Verizon FIOS then... At least with Comcast cable, the speeds there are 50, 102, and in some markets 300 something... Anyway, simply put, your console can't keep up with the internet connection. Call it a nice problem to have and move on to the next issue...
You are asking about speed on your connection in regards to a game console. Is there a particular reason? Are you having some sort of performance problem? If you really are getting 150, or even 90 mb/s into your network, there are NO games out there that should be problematic with that... You may have a latency issue which can cause slow reaction times etc... So do tell, what exact problem are you having?