Bestow Curse says

You touch a creature, and that creature must succeed on a Wisdom saving throw or become cursed for the duration of the spell. When you cast this spell, choose the nature of the curse from the following options:

• Choose one ability score. While cursed, the target has disadvantage on ability checks and saving throws made with that ability score.
• While cursed, the target has disadvantage on attack rolls against you.
• While cursed, the target must make a Wisdom saving throw at the start of each of its turns. If it fails, it wastes its action that turn doing nothing.
• While the target is cursed, your attacks and spells deal an extra 1d8 necrotic damage to the target.

A remove curse spell ends this effect. At the DM’s option, you may choose an alternative curse effect, but it should be no more powerful than those described above. The DM has final say on such a curse’s effect.

(Emphasis Mine)

I was wondering if "While Cursed, The target has vulnerability to a damage type of your choice" would be a balanced alternative curse effect. This seems like a fair trade to me because the target gets to act normally every turn and you essentially halve it's hit points, as compared to the 3rd option.

Bestow Curse says

At the DM’s option, you may choose an alternative curse effect, but it should be no more powerful than those described above. The DM has final say on such a curse’s effect.

Would "While Cursed, The target has vulnerability to a damage type of your choice" be a balanced alternative curse effect? This seems like a fair trade to me because the target gets to act normally every turn and you essentially halve its hit points, as compared to the 3rd option:

• While cursed, the target must make a Wisdom saving throw at the start of each of its turns. If it fails, it wastes its action that turn doing nothing.

Bestow Curse says

You touch a creature, and that creature must succeed on a Wisdom saving throw or become cursed for the duration of the spell. When you cast this spell, choose the nature of the curse from the following options:

• Choose one ability score. While cursed, the target has disadvantage on ability checks and saving throws made with that ability score.
• While cursed, the target has disadvantage on attack rolls against you.
• While cursed, the target must make a Wisdom saving throw at the start of each of its turns. If it fails, it wastes its action that turn doing nothing.
• While the target is cursed, your attacks and spells deal an extra 1d8 necrotic damage to the target.

A remove curse spell ends this effect. At the DM’s option, you may choose an alternative curse effect, but it should be no more powerful than those described above. The DM has final say on such a curse’s effect.

(Emphasis Mine)

I was wondering if replacing the 3rd option with "While Cursed, The target has vulnerability to a damage type of your choice". This seems like a fair trade to me because the target gets to act normally every turn and you essentially halve it's hit points.

If this question is to subjective then, Are there any variants of Bestow Curse that have been approved by any of the game designers?

Bestow Curse says

You touch a creature, and that creature must succeed on a Wisdom saving throw or become cursed for the duration of the spell. When you cast this spell, choose the nature of the curse from the following options:

• Choose one ability score. While cursed, the target has disadvantage on ability checks and saving throws made with that ability score.
• While cursed, the target has disadvantage on attack rolls against you.
• While cursed, the target must make a Wisdom saving throw at the start of each of its turns. If it fails, it wastes its action that turn doing nothing.
• While the target is cursed, your attacks and spells deal an extra 1d8 necrotic damage to the target.

A remove curse spell ends this effect. At the DM’s option, you may choose an alternative curse effect, but it should be no more powerful than those described above. The DM has final say on such a curse’s effect.

(Emphasis Mine)

I was wondering if "While Cursed, The target has vulnerability to a damage type of your choice" would be a balanced alternative curse effect. This seems like a fair trade to me because the target gets to act normally every turn and you essentially halve it's hit points, as compared to the 3rd option.