The first weapon proficiency you unlock is "kick", and for some weapons one of the first weapon attachments is "grip". Both reduce recoil, but I've often wondered if one reduces more than the other, and if the effect stacks. Since both are pretty easy to get, switching between them can of course allow for different proficiency and attachment combinations of interest (assuming they are equivalent). If they are not equivalent though, I might favor the option that had better recoil reduction - since for me in can be a real factor in my aim.
According to the Call of Duty wiki yes they do stack and Kick reduces recoil more than Grip except on the M60.
It states the following (I added the emphasis):
The Grip, again, lowers recoil for weapons and is unlocked by leveling up weapons. Also, with the new Kick Proficiency, players can combine the Grip with Kick to further decrease recoil. It is unlocked for shotguns at Weapon Proficiency Level 2 and LMGs at Weapon Proficiency Level 8. It should be noted that the Grip does not provide as much recoil reduction as the Kick proficiency, albeit on the M60, where Grip provides much better recoil reduction, but as a compromise, gives the weapons it is attached to improved hipfire accuracy.