Ability active and passive effect

In fact, if we want to be more precise, it is about when we can take profit from the penetration.

Let's say you are attacking an enemy with 100 physical protection.
If you have 0 penetration, like by default, you will 50% of your normal damage.

With Titan's Bane, all of your attacks will have 33% penetration.
That means you will be hitting as if the enemy had 67 protection, dealing about 60% of your normal damage.

With The Executioner, you are stacking a debuff on the enemy that reduces the protection.
This debuff is only applied by your basic attacks, not by your abilities.

So,

If you DON'T use basic attacks
Your damage will have 0 penetration, like by default, you will 50% of your normal damage.

If you DO use basic attacks.
Your 1st basic attack will have 0 penetration, like by default, you will 50% of your normal damage.
Your 2nd basic attack will reduce 14 protections, you will deal about 54% of your normal damage.
Your 3rd basic attack will reduce 28 protections, you will deal about 58% of your normal damage.
Any subsequent basic attack OR abilities will profit from the 42 protection reduction, dealing about 63% of your normal damage.
That debuff lasts 3 seconds, so you might want to throw at least 1 basic attack to refresh it.


Don't get fooled though, none of those 2 items is better than the other.
If you can "land" 3 basic attacks to the enemy BEFORE dealing most of your damage, then The Executioner will always be better.
Otherwise :
1- If most of your damage comes from your abilites, use Titan's Bane
2- If most of your damage comes from your basic attacks, but you plan to kill your target in less than 3 shots (like Mercury), go Titan's Bane
3- If it's about 50/50, it is about the same, the choice would be if you need attack speed in your build or not.


Finally, as if this wasn't enough, here are some things to remember, than *can influence* your choice, and are purely situational.
The Executioner gives a debuff on the enemy, while Titan's Bane is applied to your damage only

1- Every ally benefits from the enemy debuff.
So, if you are many physical gods in your team, The Executioner will do overall better during a team fight.

2- Only 1 debuff can be applied, even though 3 gods with The Executioner are hitting the same enemy. Stacks will only increase faster, that's all.
So, if your team is mostly physical and every teammates already have The Executioner, you "might" want to go for Titan's Bane.

3- Towers and Phoenix are immuned to debuff.
That means The Executioner is usless on them (aside from the attack speed) and Titan's Bane will always have better results.

4- At 200 physical protection and above, Titan's Bane will be better than The Executioner even at full stacks.
200 physical protection is considered a tank and you shouldn't focus on those anyway.
But if the enemy team is all tanky, it is something to consider, and you could consider taking both, even though it's not optimal.


Hope that was clear enough

well a passive from an active ability is the same as a normal passive

also about the exe vs titan at 200 protections they both "negate" the same amount of protections (with exe at full stacks) as the 24% + the 18 (considered as 9%) removed protections are 33% just like titans bane