I don't have the experience a lot of people on this forum have, but from the few shotgun matches I have participated in, it seemed like there were always reliability issues with 870s and Mossberg 930s. Mostly FTEs... I have never owned either (I do have shooting buddies that have owned both), so just my two cents. I hope you enjoy whatever you end up getting!
Must be firing crap ammo or not cleaning that 930 properly. The several hours of research I did on forums was overwhelmingly positive. Mine shoots like a dream.