You can always do a test hole in a piece of scrap. Most of the tubes are smaller than the drill sizes that are called for. A lot of us measure the tube and pick the drill bit that will do the job best. A larger hole is needed for back painting the blank or if you paint the tubes.
Of the two, the 13/32" would be the better choice as Dick noted. However, if you only have the 3/8" on hand, I would suggest that you test drill a scrap piece of wood and see how well the tube fits. You might have to ream it out slightly with a round file or sandpaper.
The cigar kit (WCO145) originally called out a 25/64--I made hundreds using that dimension. I think the Big Ben is the same tube, but I am not certain.