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That is the enchantment level. The base damage of a great sword will always be the same. A +1 enchantment gives a +1 bonus to hit and damage, a +2 enchantment gives +2 bonus to hit and damge. So it's slightly better. If you look on your character sheet as you switch between the two, you'll see the bonus increase by one.
Also, some creatures require an enchanted weapon to be hit. In the old D&D rules, some creatures required higher enchantments, like +2, +3 or +4 to hit. I don't know if the monsters in this game do the same.
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