APPLYING MEET/BEAT MODIFIERS

The game design involves rolling multiple dice against a target number (TN). For example, rolling 4 dice vs 5+ with results of 1, 3, 5, and 6 results in two fails (the 1 and 3) and two passes (the 5 and 6).

QUESTION: Which do you prefer, applying modifiers to the die roll results or the TN? 🤔 For example, an undesirable modifier making the roll harder to pass would be -1 if applied to the die roll or +1 if applied to the TN.

The reason for my question is that in many (most?) games using die roll modifiers and multiple dice (think 40k), the rules are written so that the modifiers apply to the die roll results but in practice players apply then to the TN for obvious practical reasons (nobody appplies the mod to each individual die rolled, that would take too long). To me, it makes more sense to write the rules by applying the mods to the TN, thus saving that informal translation.

RELATED QUESTION: If you prefer modifying the die roll result rather than the TN, should one explain in the text the typical veteran player practice of modifying the TN even when the rules are written with a DRM in mind?

Thanks in advance! You'll help settle a debate with my son! 😁