Whether you use the 107mm or the 122mm on the KV3 is dependent on your play style. The 107mm is a good gun for all ranges. Its very good for laying back and shooting and even sniping. Up close its just as accurate. Its more accurate than the 122mm. However if you like to get in close and do massive damage then the 122mm does fit that bill. Its not as accurate or as fast loading as the 107mm however and you have to get your slow poke tank in close but some people like that type of fighting.
Are you sure you aren't thinking of the 122mm on the KV? The KV is the one with the inaccurate howitzer 122mm gun. The KV-3's 122mm is basically identical to the 107mm (0.4 accuracy vs 0.39 for the 107), it just has higher damage, lower RoF and slightly better pen.
IMO the 107 is the better gun to use on the KV-3 unless you're going to buy a rammer for it.