If you play on the dedicated servers, it is just down to you skills, as you have the same weapons as every one else, so it just takes practice.  you only level up on the poor P2P lobby, so what you should do is find a good server and stick to it and you will learn how other players play the game, tactics you could use are gun and run or snip and camp depending on what weapons you use.

You have less health (or the guns are more powerful) in MW3 over BO.  So it's really easy to die and if you are lagging then it will seem like you've put a 1/2 mag into someone without a single hitmarker and they will insta kill you.  However, for someone just getting started, the action is more fast paced than BO due to the smaller maps.  I'd suggest moving around the map slowly and looking behind you frequently because there are flanking routes throughout the maps to make it easy for someone to get behind you.  Once you get used to it, things will settle down and you'll be getting kills like you're used to again.  Also, run a silencer to stay off of the radar.  It makes a huge difference when playing on small maps.