Roguelikes usually don't think in terms of dps?
A dagger traditionally does 1d4 (a four-sided dice roll, ie 1 2 3 or 4) damage, while a greatsword would be 1d10.
A broadsword could be 2d4 (two four-sided die, so 1 2 3 or 4 + 1 2 3 or 4, total result anything between 2 and 8 ).
Which comes down to a bell curves and so on and so forth.
In in-game practical terms, maybe there's a monster with 3 defense; a dagger would do 0 damage 75% of the time, while a greatsword would do 0 damage 30% of the time. However, that broadsword would ALWAYS do damage (unless you roll 1+1).
I guess that's one way to balance things.
Dungeons and Dragons balances things by giving different weapons a different chance to crit, and a different damage multiplier ON crit.
For example a Kukri or rapier will crit more often, but a Greataxe crit multiplier is higher than a rapiers.
If you talk about 20 damage in 2 turns, maybe the greatsword "locks" you into an attack for 2 turns, which means an enemy can hit you twice for every 1 swing you do. In that case I'd make it do FAR more than 20 damage, because fighting more than 1 enemy would be very deadly.
Take a look at how Brogue does weapons (pay attention to maces, axes, etc). Then take a look at how The Slimy Lichmummy does weapons.
I think you'll get a feel for balance from TSL
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