Which Katara will help me deal more damage?

So I have a level 64 Katara and am using a level 77 one.

The 64 has the following relevant stats:
39 attack
+4% crit
15% ignore defense

The 77 has the following relevant stats:
50 attack
+6% attack

Is Ignore Defense powerful enough that it actually beats the level 77 one with more attack?

No.

% Ignore Defense really isn't all that noticeable except on mobs with good amounts of PDR, so I would go with the Level 77 one.

As mentioned, go for the level 77 one. PDR is not subtracted directly from enemy defence so it's only good on monsters with very high PDR (> 50%) as you'd basically be taking off 15% of the actual PDR instead of subtracting 15% straight. Most mobs of your range only have about 5 - 10% PDR so 15% of that is only about 0.75- 1.5%.

As mentioned, go for the level 77 one. PDR is not subtracted directly from enemy defence so it's only good on monsters with very high PDR (> 50%) as you'd basically be taking off 15% of the actual PDR instead of subtracting 15% straight. Most mobs of your range only have about 5 - 10% PDR so 15% of that is only about 0.75- 1.5%.

Oh wow, good lord. I thought it was a flat reduction, which would make it so awesome. Seeing it's multiplicative it's not as great. A bit surprised that mobs at my 128 range still only have about 10-15% PDR. As for why I'm still using 8x weapons, I made the Dual Blade to be DEXless and only now have I given her some gear upgrades so she can eventually use stronger stuff. To be fair, a DB with 8x gear is still kicking major ass for me.

From what I got from a quick glimpse at the datbase, the only monsters/bosses with PDR as high as the 50%+ range are mobs/bosses involved with Chaos Zakum, Pink Bean, Cygnus, and Azwan. I assume then that THE biggest damage boost I can possibly get is +30% boss damage.

Oh wow, good lord. I thought it was a flat reduction, which would make it so awesome. Seeing it's multiplicative it's not as great. A bit surprised that mobs at my 128 range still only have about 10-15% PDR. As for why I'm still using 8x weapons, I made the Dual Blade to be DEXless and only now have I given her some gear upgrades so she can eventually use stronger stuff. To be fair, a DB with 8x gear is still kicking major ass for me.

From what I got from a quick glimpse at the datbase, the only monsters/bosses with PDR as high as the 50%+ range are mobs/bosses involved with Chaos Zakum, Pink Bean, Cygnus, and Azwan. I assume then that THE biggest damage boost I can possibly get is +30% boss damage.

I thought exactly the same thing as you before until someone corrected me which was when I went "What, so you mean Marksmanship does not in fact make me deal 25% more damage!?" And yes, 30% boss basically means something like this:

Take a 50% PDR mob. Let's assume you deal a fixed damage of 20 k for this and let's say you have either 30% PDR or 30% boss.

30% PDR x 50 = 18% so you deal 10k (1/2*20) + 1.8k damage= 11.8k.
30%*10k= 13k.

There are however circumstances where PDR gives you more bang for the buck, such as at Cygnus (70% PDR, I think?).

% Ignore is added together from all sources (Ambition, Potential, Codex, etc.) and then multiplicatively reduces the PDR of a mob. So if you have 30% Ignore from Priere D'Aria, 15% Ignore from Hob PQ codex set bonus, and 2% Ignore from Ambition, you have a total of 47% Ignore.

Normally, a boss with 70% PDR (PB/Empress) will make you do 30% of your normal damage (1-0.7 = 0.3). However, with 47% Ignore, you're looking at 1-(0.7*(1-0.47)) = 0.629 = 62.9% of your normal damage. That's an increase in damage of x2.097!

Due to the multiplicative nature of the PDR reduction, any % Ignore over 100% is useless.

I thought exactly the same thing as you before until someone corrected me which was when I went "What, so you mean Marksmanship does not in fact make me deal 25% more damage!?" And yes, 30% boss basically means something like this:

Take a 50% PDR mob. Let's assume you deal a fixed damage of 20 k for this and let's say you have either 30% PDR or 30% boss.

30% PDR x 50 = 18% so you deal 10k (1/2*20) + 1.8k damage= 11.8k.
30%*10k= 13k.

There are however circumstances where PDR gives you more bang for the buck, such as at Cygnus (70% PDR, I think?).

Using your example vs. a 50% PDR boss:
* With0% Ignore, 0% Boss) = (1-(0.5*(1-0))) * 1.0 Boss = 0.5 = 50% of your "normal" damage
* With30% Ignore, 0% Boss) = (1-(0.5*(1-0.3))) * 1.0 Boss = 0.65 = 65% of your "normal" damage
* With0% Ignore, 30% Boss) = (1-(0.5*(1-0))) * 1.3 Boss = 0.65 = 65% of your "normal" damage
* With30% Ignore, 30% Boss) = (1-(0.5*(1-0.3))) * 1.3 Boss = 0.845 = 84.5% of your "normal" damage

Or, more concretely, if you averaged 20k as your "normal" damage, then you'd be doing 16.9k vs. the 50% PDR boss.