Good advice. My 1v1 experiences are often just for fun but I can say that spawn knowledge and flanking routes are the keys to victory. That is assuming that you can shoot which you apparently can. The one that can control these things the best will have a decided advantage. Based on your story I'd say that you actually have the better gun skill but your friend has the better map control. Map control is huge.
You want to position yourself in an area that will force his respawn to somewhere that you have a good line of sight on. And, of course, you want to play mind games with him by changing your locations just enough that he has to check several corners along the way. This little distraction will leave him exposed to attack. Lastly, don't run out into the open. Save that for knife fights. Anytime that you are using guns, you need to give yourself an advantage to offset the randomness of the game and/or lag.