Why is my pizza dough so tough?
If I'm understanding correctly, the crust came out okay when you used AP flour, but was more difficult to work with and came out tough when you used bread flour.
So to answer your question, yes, you do need more water when working with bread flour than when working with AP flour. From  Serious Eats  regarding bread flour:

Will it produce a traditional Neapolitan pizza with a super-crisp, airy, and delicate crust? No. But the pizza it does produce is great for its own merits.
Bread flour requires a little more water than most other flours to produce doughs of equivalent viscosity. Because of its high protein content, some people may find bread flour doughs a little difficult to stretch — it has a tendency to bounce back. The key is to make sure that it's well-rested before you being to stretch it.

You may find that the linked article has a lot of good information about different types of flours.
From what I've read, because bread flour is a strong flour, it requires less kneading that AP flour. And a personal observation, regardless of what I am making - biscuits, a loaf of bread, a pizza dough - when I need to add more liquid later in the process rather that at the beginning, it somehow affects the results.
I would say that if you're happy with the results using AP flour, keep using AP flour. If you want to experiment using bread flour, add extra liquid at the beginning and knead less, making sure to rest the dough before forming the crust for baking.
You may also want to try other recipes. The pizza dough (for a thin crust) I make doesn't use any sugar and a very small amount of oil. And I've read that traditional Neapolitan crust uses only flour, water, yeast, and salt.