IV Stats/Judge Don't Match Up?

As the other answers state, 6 "best" is technically better than 5 "best" + 1 "very good".

But I'm not sure anyone has cleared up why the natures are causing the second Bulbasaur's Nature to drop Sp. Atk down to 5, while 'raising' defense to 6 (the same value as the neutral nature Bulbasaur).

For that we'll start by looking at how natures influence stats:

A Pokémon's Nature usually affects the value of two of its stats, ultimately increasing one of its non-HP stats (Attack, Defense, Special Attack, Special Defense, or Speed) by 10% and decreasing another by 10%.(Source)

Then consider the calculation that occurs when determining Bulbasaur's stats:

(Source)

Because your Bulbasaurs are level 1, we can drop the level piece of the equation, as well as the EV segment assuming you have no EV's applied yet. I'm going to look at Defense, which Bulbasaur has a base stat of 45 for since that's the stat that hasn't changed after being increased by nature.

This give us the equation:

((2*45+IV)/100 + 5) * Nature

Simplified giving us:

(.9 + IV/100 + 5) * Nature

Or:

(5.9 + IV/100) * Nature

Since both Judge functions are showing "Best" we know that the IV for both is 31, further simplifying to:

6.21 * Nature

For the neutral nature, this gives us a defense value of 6.21 which rounds down to 6.

For the beneficial nature, this gives us a defense value of 6.831 which rounds down to 6 (The weird brackets with only a lower horizontal bar means always round down).

TL;DR Because stats always round fractions of a stat down, the +10% from Beneficial nature isn't enough to push defense up a point, but the -10% is enough to drop Special Attack down a point.

TL,DR: Trust the judge, it's not wrong. 6 best is perfect.

Full answer: You are confusing a pokemon's regular stats with its IVs. IVs are hidden values that boost your stats, but will have almost no effect at level 1. As both of those bulbasaurs get to higher level, you would start to see a difference between their stats. The #2 bulbasaur would end up having slightly higher special defence than the #1 bulbasaur, because of the difference in IVs.

You also have a nature creating a difference between the two bulbasaurs. The #1 bulbasaur has a neutral nature that does not raise or lower any stats, shown by the lack of any blue or red highlighting. the #2 bulbasaur has a nature that raises defense and lowers special attack, so as they increase in level that would cause a stat difference as well. When you reach end-game after the Championship, you'll be able to buy items that change nature to move the red and blue highlighting to boost stats you want and lower stats that don't matter to you.

There is no contradiction. IVs are hidden values that add up to 31 into a stat at level 100. IVs are not your stats at level 1.

The red and blue highlights show which stats are boosted and lowered by the Pokémon's nature, they have nothing to do with IVs.

I suggest you read more about what IVs are, for example on Bulbapedia.