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In the group I am playing with, my character is a level 20 Sorcerer with the Draconic Bloodline. Through this Bloodline, I obtain a special attack of Breath Weapon and automatic spell of Form of the Dragon III

The description for the bloodline special attack says

At 9th level, you gain a breath weapon. This breath weapon deals 1d6 points of damage of your energy type per sorcerer level. Those caught in the area of the breath receive a Reflex save for half damage. The DC of this save is equal to 10 + 1/2 your sorcerer level + your Charisma modifier. The shape of the breath weapon depends on your dragon type (as indicated on the above chart). At 9th level, you can use this ability once per day. At 17th level, you can use this ability twice per day. At 20th level, you can use this ability three times per day.

As I am level 20, the breath weapon will deal 20d6 three a day

However, if I were to transform into a dragon using Form of the Dragon III, it appears my breath weapon is no where near as powerful

You can use the breath weapon as often as you like, but you must wait 1d4 rounds between uses. All breath weapons deal 12d8 points of damage and allow a Reflex save for half damage. Line breath weapons increase to 100-foot lines and cones increase to 50-foot cones.

While in dragon form, the breath attack only deals 12d8 every 1d4 rounds.

Why are there differences in how much damage the breath weapons deal?

Sources:

Form of the Dragon

Draconic Bloodline

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Because of their recharge and shape.

The Draconic Bloodline breath weapon is more powerful (70 average damage vs 54) because it can only be used 3 times per day and affects a smaller area. The Form of the Dragon breath weapon can be used every 1d4 rounds, and affects a 50' cone or 100' line, versus the bloodline breath weapon's 30' cone or 60' line.

Note that as far as I can tell nothing stops you from using your Draconic Bloodline breath weapon while you're in Form of the Dragon; it's not that your breath weapon suddenly does less damage, it's that you gain another breath weapon with lower damage but a much faster recharge and larger area.

From the PFRD (emphasis mine):

Form of the Dragon I
You become a medium chromatic or metallic dragon. You gain... a breath weapon. Your breath weapon and resistance depend on the type of dragon. You can only use the breath weapon once per casting of this spell. All breath weapons deal 6d8 points of damage and allow a Reflex save for half damage. In addition, some of the dragon types grant additional abilities, as noted below.

"All breath weapons", in all 3 versions of the spell, means "any breath weapon you got from this spell, regardless of which kind of dragon you chose", rather than "all abilities you have that happen to be called a breath weapon".

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  • \$\begingroup\$ Ah ha, I never would have thought you could use both types while in dragon form. I assumed that the weapon was replaced, not gained. \$\endgroup\$ – Wondercricket Feb 12 '16 at 19:31

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