I have a +5 broadsword, but now that I'm here at the smith, even bumping it to +6 it's nowhere near as strong as the drake sword. Am I missing something about it being well past it's usefulness?
Stat scaling is what you are missing, the base number you are seeing may be lower than the Drake Sword, but it gets a bonus from your weapon stats (STR and DEX). So you have the base damage plus the scaling bonus based on your stats and how well upgraded the weapon is +5,+10, with +15 being the best for STR/DEX scaling.
The Drake Sword has no stat scaling whatsoever, so any points invested in STR or DEX past the minimum requirements to wield are literally wasted on a weapon with no stat scaling.