Does COX limit or cap bandwidth speeds?

Unsure if there is a way to measure this speed, or if there is a site to check, but I have been told that the amount of speed compared to the bandwidth COX provides is very different? 

I am a heavy gamer.  I pay for the highest speed available right now that COX offers in  my area - 300DL 30UL.

I have tried to play COD BLOPs 3 - when I run a speed test through my XBone it does tell me that my speeds are good and where they should be, DL & UL.  When I run the network portion in the setting tab on BLOPs 3, it is not a speed test but a BANDWIDTH SPEED.  This speed is only 4011kbps.  This is a very poor speed even if it is a "bandwidth test/speed"  I have read other forums where people are getting 10000- 20000kbps.  I have never seen mine over 4200kbps. 

If I am paying for the 300Mbps or "Ultimate" Service, shouldn't I be getting a much higher speed? 

Hardware: Motorola SB6183 modem, Nighthawk AC1900, Xbox One