Well...I think screws are stronger than nails...But I think a good quality wood glue is stronger than either, and the most important component of assembly!
I use Titebond III, a lot of folks will tell you Titebond II is sufficient, and they're "probably" right, but I like a little over-engineering!
If you are going to use glue, I think nails are more than sufficient...If you're not going to use glue, I think screws is the better choice, but still don't think it will match up to basically any reasonable fastener used in conjunction with a quality glue....But understand, as with EVERYTHING in Beekeeping, opinions do vary!