If you have the time and patience, go with screws. As BJ and someone else said above, they will "pull" the two panels together. But, unless you are using SPAX screws (world's greatest invention for MDF screwing IMO), you will need to predrill which can be time consuming and a hassle.
This is where you need to decide what's more important, your time, or knowing the box was done better, cause odds are you won't hear or see a difference with brad nails or screws. On the meter, maybe, but I don't know, I'm not a .1 chaser //content.invisioncic.com/y282845/emoticons/tongue.gif.6130eb82179565f6db8d26d6001dcd24.gif.
This is where you need to decide what's more important, your time, or knowing the box was done better, cause odds are you won't hear or see a difference with brad nails or screws. On the meter, maybe, but I don't know, I'm not a .1 chaser //content.invisioncic.com/y282845/emoticons/tongue.gif.6130eb82179565f6db8d26d6001dcd24.gif.