Probability of improving to a six badugi in one draw if you draw three is (I think)
15*8*3/48/47/46=0.00347, about one in 288.
Probability of improving to a seven badugi in one draw if you draw two is (I think)
15*8/48/47=0.0532, about one in 19.
Of course there are two more draws possible in each case... but just on the basis of the first draw you're about 15 times more likely to end up with a seven badugi if you draw two than ending up with a six badugi if you draw three.
Meanwhile it's unlikely either one of your one-draw opponents will end up with a six badugi or better.
(I'd draw two, not three... but I don't know this game well).
Buzz