[RPG] How does two weapon fighting calculate the offhand attack

Two-Weapon Fighting does not reduce the penalties from Flurry of Blows, since Flurry is not the same thing as fighting with two weapons:

Two-Weapon Fighting: If you wield a second weapon in your off hand, you can get one extra attack per round with that weapon.

Unarmed Strike: A monk’s attacks may be with either fist interchangeably or even from elbows, knees, and feet. This means that a monk may even make unarmed strikes with her hands full. There is no such thing as an off-hand attack for a monk striking unarmed. A monk may thus apply her full Strength bonus on damage rolls for all her unarmed strikes.

Flurry of Blows: When unarmored, a monk may strike with a flurry of blows at the expense of accuracy. When doing so, she may make one extra attack in a round at her highest base attack bonus, but this attack takes a -2 penalty, as does each other attack made that round.

The only thing Two-Weapon Fighting and Flurry have in common are that they grant an extra attack. The Two-Weapon Fighting feat only reduces the -6/-10 penalties for fighting with a second weapon in your off-hand, but even with flurry a monk using unarmed strikes has no off-hand. All his unarmed strikes are considered on-hand.

Interestingly, according to the D&D 3.5 FAQ, a monk can use Two-Weapon Fighting to make an extra off-hand attack, even on top of Flurry, but the penalties from Two-Weapon Fighting stack the penalties from Flurry:

Can a monk fight with two weapons? Can she combine a two-weapon attack with a flurry of blows? What are her penalties on attack rolls?

A monk can fight with two weapons just like any other character, but she must accept the normal penalties on her attack rolls to do so. She can use an unarmed strike as an offhand weapon. She can even combine two-weapon fighting with a flurry of blows to gain an extra attack with her off hand (but remember that she can use only unarmed strikes or special monk weapons as part of the flurry). The penalties for twoweapon fighting stack with the penalties for flurry of blows.

In other words, a first-level monk with the Two-Weapon Fighting feat has four options: make one attack at +0, Flurry for two attacks at -2/-2, TWF for two attacks at -2/-2 (but one of those is off-hand and applies only half Strength modifier), or combine Flurry and TWF for three attacks at -4/-4/-4 with one of those an off-hand attack. You can't use the Two-Weapon Fighting feat on its own to reduce Flurry's penalties.

It really depends. for a cleric, they are functionally identical.

Here are the damage expressions:

Two hander: 2d6 + str

TWF: 1d6 + str, 1d6

Literally exactly the same when you factor in that your to-hit is going to be the exact same number for both. You only get your Divine strike (I think War domain gets that at 8 and 14 like the Life cleric does) on the first hit so that does favor TWF slightly at 8 and more at 14.

The next thing to look at is the action economy. TWF uses your bonus action every round. Whereas GWF leaves it free. You've got some bonus action spells you might want to use.

Lastly, there is feat selection. A melee cleric is MAD (Multiple Ability Dependent) so you might not want to actually pick up a feat and let both your stats run up to 20, but if you could settle for an 18 str, you might want to pick up the feat related to your fighting style. The GWF feat gives you extra attacks, but the TWF feat lets you wield one handed weapons rather than only light weapons and boosts your AC a bit.

Really, looking at the numbers, the decision is entirely up to you and how you want to play the character, they are quite similar. I give the damage edge to TWF, and the action economy edge to GWF. Ultimately though, at high levels, your cantrips might end up doing more damage than your weapon attacks anyways.