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The magical effect of bless is:

Whenever a target makes an attack roll or a saving throw before the spell ends, the target can roll a d4 and add the number rolled to the attack roll or saving throw.

When determining “which effect is more potent”, this is what we are evaluating. To be precise, the result of the d4 roll is not the effect we are evaluating, the spell description is. It is unambiguous that determining which effect is more potent is done before the effects are applied: rolling the dice is applying the effect since the effect says roll a d4, and deciding afterwards requires rolling twice, something explicitly forbidden in the rule cited:

he or she doesn’t get to roll two bonus dice.

To put it another way, we can use a reductio ad absurdum argument to get the right approach.

(1) Suppose we determine which bless to apply after seeing which rolls the greater bonus.

(2) We roll two dice.

(3) This contradicts the rule cited “he or she doesn’t get to roll two bonus dice”.

(4) Therefore we determine which bless to apply before seeing which rolls the greater bonus.

The magical effect of bless is:

Whenever a target makes an attack roll or a saving throw before the spell ends, the target can roll a d4 and add the number rolled to the attack roll or saving throw.

When determining “which effect is more potent”, this is what we are evaluating. To be precise, the result of the d4 roll is not the effect we are evaluating, the spell description is. It is unambiguous that determining which effect is more potent is done before the effects are applied: rolling the dice is applying the effect since the effect says roll a d4, and deciding afterwards requires rolling twice, something explicitly forbidden in the rule cited:

he or she doesn’t get to roll two bonus dice.

To put it another way, we can use a reductio ad absurdum argument to get the right approach.

1. Suppose we determine which bless to apply after seeing which rolls the greater bonus.
2. We roll two dice.
3. This contradicts the rule cited “he or she doesn’t get to roll two bonus dice”.
4. Therefore we determine which bless to apply before seeing which rolls the greater bonus.

The magical effect of bless is:

Whenever a target makes an attack roll or a saving throw before the spell ends, the target can roll a d4 and add the number rolled to the attack roll or saving throw.

When determining “which effect is more potent”, this is what we are evaluating. To be precise, the result of the d4 roll is not the effect we are evaluating, the spell description is. After all, it is unambiguous that determining which effect is more potent is done before the effects are applied; deciding afterwards requires rolling twice, something explicitly forbidden in the rule cited:

he or she doesn’t get to roll two bonus dice.

To put it another way, we can use a reductio ad absurdum argument to get the right approach.

(1) Suppose we determine which bless to apply after seeing which rolls the greater bonus.

(2) We roll two dice.

(3) This contradicts the rule cited “he or she doesn’t get to roll two bonus dice”.

(4) Therefore we determine which bless to apply before seeing which rolls the greater bonus.

The magical effect of bless is:

Whenever a target makes an attack roll or a saving throw before the spell ends, the target can roll a d4 and add the number rolled to the attack roll or saving throw.

When determining “which effect is more potent”, this is what we are evaluating. To be precise, the result of the d4 roll is not the effect we are evaluating, the spell description is. It is unambiguous that determining which effect is more potent is done before the effects are applied: rolling the dice is applying the effect since the effect says roll a d4, and deciding afterwards requires rolling twice, something explicitly forbidden in the rule cited:

he or she doesn’t get to roll two bonus dice.

To put it another way, we can use a reductio ad absurdum argument to get the right approach.

(1) Suppose we determine which bless to apply after seeing which rolls the greater bonus.

(2) We roll two dice.

(3) This contradicts the rule cited “he or she doesn’t get to roll two bonus dice”.

(4) Therefore we determine which bless to apply before seeing which rolls the greater bonus.

The magical effect of bless is:

Whenever a target makes an attack roll or a saving throw before the spell ends, the target can roll a d4 and add the number rolled to the attack roll or saving throw.

When determining “which effect is more potent”, this is what we are evaluating. To be precise, the result of the d4 roll is not the effect we are evaluating, the spell description is. After all, it is unambiguous that determining which effect is more potent is done before the effects are applied; deciding afterwards requires rolling twice, something explicitly forbidden in the rule cited:

he or she doesn’t get to roll two bonus dice.

The magical effect of bless is:

Whenever a target makes an attack roll or a saving throw before the spell ends, the target can roll a d4 and add the number rolled to the attack roll or saving throw.

When determining “which effect is more potent”, this is what we are evaluating. To be precise, the result of the d4 roll is not the effect we are evaluating, the spell description is. After all, it is unambiguous that determining which effect is more potent is done before the effects are applied; deciding afterwards requires rolling twice, something explicitly forbidden in the rule cited:

he or she doesn’t get to roll two bonus dice.

To put it another way, we can use a reductio ad absurdum argument to get the right approach.

(1) Suppose we determine which bless to apply after seeing which rolls the greater bonus.

(2) We roll two dice.

(3) This contradicts the rule cited “he or she doesn’t get to roll two bonus dice”.

(4) Therefore we determine which bless to apply before seeing which rolls the greater bonus.