Which is better: 1d8+1 or 1d6+2?

Which is better: 1d8+1 or 1d6+2?

1d6+2.

More readily available die, cheaper at any given level of quality, more easily stored, less potential to be painful when stepped on barefoot.

1d6+2
both have the same overall damage, but the d6 means a smaller damage range, so if you get screwed by bad rolls it won't be as bad. yes you have a lower max damage with the d6, but the tradeoff is worth it.

depends on what the target number is

without doing maths, 1-2 doesn't matter, 3-4 d6 is better, 8-9 d8 is better.

Depends.
If a normal enemy has 7 to 9 HP, the d8 is more likely to one-shot them. If a normal enemy has 5 or fewer HP, the d6 has better chances. If the enemy has more than 9 HP, subtract increments of 5.5 until they don't, then see above.
If you're talking DCs instead of damage rolls, same thing applies except don't subtract.

Casual math get out.

The question wasn't "which is better for killing things in one hit", the question was "which is better". A smaller range means a more predictable result, which allows for better planning.

Better planning means fuck and all in the face of better results.
If 1d8+1 has a 37.5% success rate and 1d6+2 has a 33.3% success rate, the d6 is predictably inferior.

Better planning for what?

You either know the target number/DC, in which case you can determine which dice is better, or you don't, in which case what the fuck are you planning for?

1d6+2

Lowest damage you can roll is 3.

It's a measure of your personality. A pessimist thinks 1d6+2 is better because you're screwed over less by small rolls, while an optimist thinks 1d8+1 is better because you can roll higher.
>1d6 if you're a beta cuck
>1d8 for real alpha males