totally depends on who you are working with, and working for. Ask people who are already doing the jobs what they think about the job, and their direct supervisor. Even if you have to go to the store at 2:00 a.m. it's worth finding out.
Drug/GM is just another department within the store (GM stands for General Merchandise). They maintain obviously Over The Counter (OTC) medications for cold/flu etc.. as well as all of the furniture, holiday items etc.. The only real difference between night stock and the Drug/GM department, other than the hours, is the pay scale. Night stock employees receive a premium for working those types of hours (usually 9pm - 5am/ 10pm- 6am etc..) Other than that its all about who you are working for. If you are new to the store, then you probably don't know many people. Asking who is better to work for is all just a matter of personal opinion. Some may like the Drug/GM department manager, others may have personal reasons that they do not. If you can take the hours and have no scheduling restrictions, I would personally start in night stock. There are several key advantages but mainly, ITS AT NIGHT! You do not have nearly as much customer interaction, which allows you to focus on your duties at hand and gives you more freedom at work. If you are more of an extroverted person, you should consider drug/gm. The premium, if I'm not mistaken, is about .50 cents an hour more. You may not think .50 cents is all that much, but it adds up to about $20 bucks a week. That's extra fuel in your gas tank!
GM is a pain in the ass. Not all Krogers are the same. Division difference is like 2 different companies. Zone 1(Nashville) only gets $0.50 night premium at night beginning at !2 midnight till 6 or 7am. IMO Zone 1 is a complete disaster compared to Delta. PT's are taken care of better in Delta, but thats the Unions fault.