Sorry for the delayed response! I didn't see the message.
The advantages of a screened bottom board include the ability to observe the colony from below, add more ventilation (maybe not an advantage), and the supposed benefit of Varroa mites falling through the screen to the board below. Personally I don't use screened bottom boards on any of my hives (25 or so) and my bees do fine. However, due to the overwhelming number of requests we've had for SBB, we've begun to offer them.