Dueling gives you immediate benefits to your chance to hit and chance not to get hit, these bonuses are significantly better for the first half of the game, near the endgame characters that are fully specialised in melee combat benefit more from Two Weapon Fighting but the extra damage isn't enough to be worth it

The Two Weapon Fighting Feat



















Benefit: One extra attack with the offhand weapon per round
Dual Wield Penalty:

• Two-Weapon Fighting -6 (main hand) / -6 (off hand)
  
• Improved Two-Weapon Fighting -4 (main hand) / -4 (off hand)
  
• Master Two-Weapon Fighting -2 (main hand) / -2 (off hand)

The Dueling Feat

+1-3 Attack +1-3 Defence when using a single weapon
This is controversial but in my experience Dueling is better than Two Weapon Fighting, on paper Two Weapon Fighting looks superior because of the extra swing per round which equals more damage but in practicality the bonuses from Dueling are better, lets compare,

Why Dueling is better:

Two Weapon Fighting example with a Balanced Double Bladed Lightsabre at max level with no crystals and 30 Strength:

• Attack 1 (Base): 2d10+10 Damage, -2 Attack
  
• Attack 2 (Offhand): 2d10+10 Damage, +0 Attack
  
• Attack 3 (Flurry): 2d10+10 Damage, -2 Attack
  
• Attack 4 (Force Speed): 2d10+10 Damage, -2 Attack
  
• Attack 5 (Force Speed): 2d10+10 Damage, -2 Attack

Total:

• 8d10+40 Damage (80), -2 Attack
  
• 2d10+10 Damage (20), +0 Attack

Dueling example at max level with no crystals and 30 Strength:

• Attack 1 (Base): 2d8+10 Damage, +3 Attack
  
• Attack 2 (Flurry): 2d8+10 Damage, +3 Attack
  
• Attack 3 (Force Speed): 2d8+10 Damage, +3 Attack
  
• Attack 4 (Force Speed): 2d8+10 Damage, +3 Attack

Total:

• 8d8+40 Damage (72), +3 Attack

On paper the 100 Damage looks so much better compared to 72 damage but in reality you are not putting out all that damage because you are missing more often, lets calculate how much damage we do to a real enemy in the most favourable conditions possible for a Two Weapon Fighting user:

Darth Malak (Star Forge)
Defence: 38

Our average offensive power with Two Weapon Fighting (30 STR):
1d20
+20 (Level 20 Soldier/Guardian)
+10 (30 Strength)
8d10+40+44 Damage (124), +36 Attack, Hit roll = 37-56 (95% hit rate)
2d10+10+11 Damage (31), +34 Attack, Hit roll = 35-54 (95% hit rate)
Average Damage = 124*0.95 + 31*0.95 = 147.25 DPS *1.05 Crit chance = 154.6 DPS
(Crystals: Solari + Upari)

Our average offensive power with Dueling (30 STR):
1d20
+20 (Level 20 Soldier/Guardian)
+10 (30 Strength)
8d8+40+44 Damage (116), +39 Attack, Hit roll = 40-59 (95% hit rate)
Average Damage = 116*0.95 = 110.2 DPS * 1.1 Crit chance = 121.2 DPS
(Crystals: Solari + Upari)

A 27.6% damage boost for the Two Weapon Fighting user, even though Two Weapon Fighting is slightly better at the end of the game the downside in the early game of missing a large percentage of your attacks makes the extra endgame power not really worth it.

Dueling benefits you more in the early game when you will find it hard to hit with Two Weapon Fighting because of the very large penalties to hit, the +3 to Defence will also keep you alive much better.

On a character that isn't min-maxed to the extreme for melee combat like the example above Dueling is also far superior and will often result in more DPS than Two Weapon Fighting.

On the opposite spectrum here is an early game example of combat against a difficult opponent:

Sith Governor (Sith Base - Taris)
Defence: 19

Our average offensive power with Two Weapon Fighting:
1d20
+8 (Level 8 Soldier)
+2 (14 Strength)
-4 Main hand / -4 Off hand (Improved Two Weapon Fighting)
Echani Ritual Brand
2d6+3 Damage (9), +9 Attack, Hit roll = 10-29 (60% hit rate)
2d6+3 Damage (9), +7 Attack, Hit roll = 8-27 (50% hit rate)
Average Damage = 9*0.6 + 9*0.5 = 9.9 DPS *1.05 Crit chance = 10.4 DPS

Our average offensive power with Dueling:
1d20
+8 (Level 8 Soldier)
+2(14 Strength)
+2 (Improved Dueling)
Prototype Vibroblade - Upgraded
1d10+6 Damage (11), +15 Attack, Hit roll = 16-35 (80% hit rate)
Average Damage = 11*0.8 = 8.8 DPS *1.1 Crit chance = 9.7 DPS

Only a 7.2% damage increase, forgoing it in favour of Dueling for +Defence will ensure you get hit less and therefore are more likely to survive and defeat the enemy.

Lets determine the effectiveness of +Defence against this example enemy,

Our Defence:
10 - Base
7 - Light Battle Armor
2 - Dexterity Bonus
2 - Dueling
Without Dueling = 19
With Dueling = 21

Sith Governor Attack = 14
Hit roll = 15-24
Chance to hit without Dueling = 80%
Chance to hit with Dueling = 70%
VP = 96
Effective VP without Dueling = 96/0.8=120
Effective VP with Dueling = 96/0.7=137
= 14% Increased durability
The effectiveness of the extra defence increases exponentially the more defence you have / the less attack the enemy has, so lets test this with an weaker enemy in the same area,


Sith Trooper Attack = 7
Hit roll = 8-27
Chance to hit without Dueling = 60%
Chance to hit with Dueling = 50%
VP = 96
Effective VP without Dueling = 96/0.6=160
Effective VP with Dueling = 96/0.5=192
= 20% Increased durability

Finally, anecdotally people who speedrun the game generally* (corrected) go for Dueling over Two Weapon Fighting.
https://www.youtube.com/watch?v=04eajgeTrsk