It seems that for most of the time during the day the big one didn't care about the things on the web, he was up on the branch hidden between the leaves and I saw him actively on the web only in the morning and in the evening, that fly on the photograph was also caught in the midday and he didn't come ... but even when he was active and eating, the small spiders were around at some distance and he was not aggressive towards them.
On this photograph of bad quality made with the flash at dawn, not much light were in the woods, you can see, not very clear but you can :), the small spider ...

This is what I saw ... I don't know the scientific facts behind this story and these behaviors

This is just what I saw while visiting and photographing the web

And :) thanks for the comment, this was a good question.