I prefer Counter Strike to COD, but I have played more CS than COD. And I'm better with a mouse than I am with a controller. You can get a free program called Aim Lab on Steam to practise your aim and speed. The reason CS is hard is because a lot of players are quick and accurate with a mouse.
CS over COD for sure, its f2p so you can give it a try before you buy anything the game has to offer. There is a definite learning curve and don't expect to be accurate at ALL if you just hold down the button to shoot.