Without seeing the design or anything about what the 6mm drawer bottoms might be supporting, I'm going to suggest that 6mm is plenty (because the odds are in my favor). If you have one bottle per drawer, 6mm is more than adequate. If you have 20 bottles per drawer with no other support, 6mm may not be adequate.
For my wine racks, there are no "bottoms." There are only fronts, backs, and sides. (I tried to add smiley faces, etc. but I am emoticon impaired)