Depends on your playstyle.
I've used both for a long time and prefer to use AKS. To use K1A1 effectively, it is to aim for chest/head, as comparing the damage between them, AKS can range very easily when used correctly.
Mods I prefer to use on AKS
-Burst Barrel (-1 Accuracy +2ROF)
-Ergonomic Grip (+1 Accuracy)
-Stab Trigger (-1 ROF +2 Stability)
Using these mods, you're not sacrificing anything statistically, as these mods provide overall +1 stability and rate of fire.
Mods I prefer to use on K1A1
I prefer to use these mods because the K1A1 doesn't bloom as much, and the high stability and high ROF really makes it a good weapon. Imo.
If you can handle the AKS' high bloom and moderate recoil level well enough, I wouldn't consider the K1A1.
I'd say the K1A1 is an alternative of the AKS, sacrificing damage & damage @ range for less recoil and bloom.
But as a secondhand choice, I'd suggest the MP7.