Hmm, because the oldforums is gone, I’m not 100% certain on the calculations, but I am fairly certain that is not how its calculated.
IIRC, the +150% on the Bessie is additive to the critical bonus on the Sniper/Ranger class mod (which multiplies the bonus on your sniper rifle).
Hence, with a Sniper class mod, the calculations would go like:
2*(1+1.5+1) =7
as opposed to a Jakobs Thunder
2*(1+1) = 4
When calculated in conjunct with Mordecai’s other skills on a bandit enemy:
Bessie Critical Hit = 1 + 1.5 (EnemyZoneBonus) + 0.75 (Deadly) + 7 (Sniper Critical Hit) = 10.25
as opposed to a Purple Thunder
Thunder Critical Hit = 1 + 1.5 (EnemyZoneBonus) + 0.75 (Deadly) + 4 (Sniper Critical Hit) = 7.25
Of course on a Lance Enemy, the difference is even more indistinguishable
Bessie Critical Hit = 1 + 5 (EnemyZoneBonus) + 0.75 (Deadly) + 7 (Sniper Critical Hit) = 13.75
Thunder Critical Hit = 1 + 5 (EnemyZoneBonus) + 0.75 (Deadly) + 4 (Sniper Critical Hit) = 10.75
That said, the Bessie will still be the best Pump-Action Sniper Rifle because its Legendary Effect means it will still exceed a purple Thunder in base damage by a little bit and that additional crit means it will always win in calculations.
For Mordecai:
If using the Bessie against Bandit enemies (which you should), by calculations, the Sniper class mod should still win out against the Gunfighter and Ranger. IIRC, the Sniper still won by a tiny bit against Lance. I wouldn’t use the Bessie against Lance though. Any decent corrosive sniper should outperform it when utilizing an Assassin class mod.
In general, I would think that for per shot efficacy, Mordecai would win whenever Relentless procced, but Lilith with a Spectre class mod would perform better passively because of her BulletDamage buffs from High Velocity and Enforcer. A Warmonger Brick with +4 Revenge should be superior on kill if Relentless does not proc for the same reason as well. Loaded, Fast Hands and Killer do give Mordecai an advantage in utilizing a 3 shot version though.