Help with some mathematical comparisons

So I'm in the middle of designing a board game that will have deck building and dice rolling elements in it. After some brain storming, I came up with a dice rolling system that had room for different methods of influencing it.

As far as Dice Rolling, the system works by having a target number. Hitting this number exactly provides you one success. Rolling higher gives additional successes equal to the difference between the number rolled and the target number. For example, if you had to roll a five and you rolled an 8, you'd have three successes. In this game, we're identifying these additional success as Threshold Success.

A related mechanic is that you start rolling a D6 in this game, but you can upgrade the dice you roll a "leveling up" system. You start with a D6, but you can end up with a D12 through upgrading.

Now we have three major types of effects that modify how successful you were.

1. A bonus to your dice roll. This is the most power, and as such, has an inherently lower number. We call this a Straight Bonus
2. A bonus that is capped by your Dice's highest number. So it's really good to make sure you do well, but won't provide you Threshold Successes. We call this a Natural Bonus.
3. A bonus to Threshold Success if the roll was successful. So in the above example, if you played a card that was +2 Threshold Successes, you'd have six Threshold Success instead of just 3. We call this a Threshold Bonus.

Now players will choose characters when they start, each belonging to different groups. Originally, each group was going to have access to the their own version of the above cards. But then I wondered if each of the three groups could each have one of the top three be an optimal Primary, with a less useful Secondary, and a near useless Inferior.

So for example.
Group A: Excels at Straight Bonus, Adequate at Natural Bonus, Inferior at Threshold Bonus.
Group B: Excels at Natural Bonus, Adequate at Threshold Bonus, Inferior at Straight Bonus.
Group C: Excels at Threshold Bonus, Adequate at Straight Bonus, Inferior at Natural Bonus.

I really like the idea of having each group be better at certain types. It makes the choices players make very apparent. But the question becomes, how do we make that balanced? Should I instead go with the easier "Everyone gets an Primary, Secondary, and Inferior version of each" method instead? Anyone have any thoughts on the matter? If you have math or sites where I can plug in the numbers myself, I'd be very appreciative.

Thanks!