It partly depends on how many pluses you have on your 1H, 2H and shields.
Also, against human sized or one square enemies the difference in damage potential is not that big.
In practice I usually go for 1H + shield, with a 2H as backup weapon.

There are certain points in the game where, at least in my experience, you'll have access to two handed swords +2 as well as at least one ring of protection +1, while your best longsword is +1. With that in mind, I go for the two-handed sword every time, because the drop off in your armor class isn't as big a deal as the bonus to hit and the additional damage you can do to larger enemies.

That said, I have a fighter using a +1 shield and +2 mace who reliably does decent damage and rarely gets hit. I'm sure there's a sweet spot that balances the tradeoff between damage and defense, but I've done pretty well with the two-handed sword approach.

I carry both, as the OP said. Longsword for one-square icon monsters, two-handed sword for two or four-square icon monsters.

Damage for smaller monsters is 1-8 (average 4.5) longsword, 1-10 (average 5.5) two-handed. So two-handed usually isn't worth the AC change, especially if you have a magic shield.

Damage for larger monsters is 1-12 (average 6.5) longsword, 3-18 (average 10.5) two-handed. At that point it becomes a risk-benefit tradeoff.