Protecting Your Documents: Safe Deposit Box or Online Storage?

For $40 a year, I can rent a 3" x 5" x 24" safe deposit box for storing valuables at a local bank. This is where I'd put my birth certificate and social security card, a copy of my passport, and assorted coins.

If you were me, would you rent the box knowing you could only access it when the bank is open?

Or, would you digitize your documents by scanning them into computer files, encrypting the files, and uploading them to something like Amazon S3 for a fraction of the annual cost and for a system that will never be affected by fire or flood damage?

I carry my social security card in my wallet, and keep my birth certificate in the same apartment location as my passport. Neither is safe, but is it better to use a bank's service or use the web? Which would you do? Which do you already do?