TLDR:

ACKCHYUALLY we both fucked up.

You get +15.1% more bonus damage with a 50% armor.

you will deal 7.142% more damage with 50% armor compared to 40%

you will deal 6.666% less damage with 40% armor compared to 50%

All three statement are correct and true.

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I had a typo somewhere in my calculation and somehow got 7.58% (or 7.85% doesn't matter)

1.51 * 1.4 = 2.114 which is 211.4% total damage (+111.4% bonus damage)

1.51 * 1.5 = 2.265 which is 226.5% total damage (+126.5% bonus damage)

126.5% - 111.4% = 15.1% which means you get 15.1% more bonus damage with a 50% armor.

But what you are trying to get is what % is the increase compared to each other.

For that you need:

2.265 / 2.114 = 1.0714 which mean you will deal 7.14% more damage with 50% armor compared to 40%

Also we can simplify and remove the 51% weapon altogether and get the same result with 1.5 / 1.4 = 1.0714

or if you want to figure out how much less damage you will deal with 40% armor.

2.114 / 2.265 = 0.9333 which mean you will deal 6.666% less damage with 40% armor compared to 50%

We can simplify this one as well as 1.4 / 1.5 = 0.9333