When you use the boosted dirt to break a dirt or grass block, you get +1 dirt and +1 grass per level of boost (so +3 of each at B3).

The double drops multiplier only applies to the extra blocks of the type you broke. So if I break a grass Block while holding a B3 Dirt, it gives me 8 dirt and 3 grass blocks, when it should be giving me 8 dirt and 6 grass blocks.

Tested this multiple times immediately before I posted this message.