LogFAQs > #945219228

It's easiest to tabulate.
Single 2d6: 0%, 3%, 8%, 17%, 28%, 42%, 58%, 72%, 83%, 92%, 97%, 100%
Reroll 2d6: 0%, 5%, 16%, 30%, 48%, 65%, 82%, 92%, 97%, 99%, 99%, 100%

Using the +1 item is equivalent to moving one step to the right. Using a +2 item is equivalent to moving two steps to the right, and so on. Using the reroll item is equivalent to moving from the top row to the bottom row.

From here we can see that if your unmodified success condition is
2d6 >= 13, 12 or 11 (0%, 3% or 8% chance), it's better to take a +1 modifier than a reroll.
At 2d6 >= 10 or easier (17+% chance), it's better to take a reroll than a +1 modifier.
Until 2d6 >= 7 (58% chance), it's better to take a +2 modifier than a reroll. At 2d6 >= 6 (72% chance), they become basically equal.
At 2d6 >= 4 the +2 modifier becomes better again since it gives 100% chance. At 2d6 >= 3 the +1 modifier becomes better than the reroll since it gives 100% chance.
A +3 modifier is always superior.

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