- Str sword & board is no better than Dex sword & board at hitting people thanks to the rapier being as good as the longsword. And it's worse >90% of the rest of the time.
I think strength sword and board is substantially better for 4 reasons:
1. Melee Weapons - the strength sword and board can use a Rapier, Longsword, Battleaxe, Pick, Morningstar, Flail or warhammer and do 1d8 damage. The dex sword and board can only use a Rapier. Also a host of d6 melee weapons are available and there are only two with a dex guy. This versatility matters a lot once magic weapons start showing up. While wielding that +1 Trident might not be what you had in mind at character build, it will do more damage than a non-magic Longsword or Rapier.
2. Missile weapons - A sword and board is usually going to want to melee, but occasionally they are going to need to hurl something. All of the weapons you can use as a sword and board are thrown and usable with strength. Only a couple of them (dart, dagger) are finesse and usable with dexterity. Further the damage is higher, 1d6 vs 1d4.
3. Bludgeoinging damage - While longsword is the trope for a sword and board, and a Rapier also does 1d8, the best weapon for a sword and board actually a flail or a warhammer, especially at low levels. At low levels you are usually going to run into fair numbers of enemies that are either vulnerable to bludgeoning damage or resistant to piercing and slashing.
4. Armor - high strength means heavy armor without sacrificing movement. This in turn means a higher AC. It is only 1 point, but then add that your strength is higher so you don't hit your encumberence limit as soon either.
Individually these are all relatively minor, but taken together they make a strength swordmore powerful in combat than a dex sword and board IMO.