What are the differences between normal version and director's cut version of episode 6? According to Wikipedia - List of Gurren Lagann episodes, episode 6 has 2 versions:


The normal version which is first aired on May 6, 2007 in Japan, titled 

"Sit in the Hot Tub 'Till You're Sick!!" (てめえら全員湯あたりしやがれ!!)
The director's cut version, which is released on DVD, having a different title

"There are Some Things I Just Have to See!!" (見てえものは見てえんだ!!)


What are the differences between the 2 versions?
According to the wiki:


  The uncut version of this episode features more explicity such as:
  
  
  More of Yoko's breasts are revealed. At the end of the episode, her top falls off completely-although we still don't see anything.
  Gimmy's penis is briefly shown. (This is actually not seen as taboo in Japan, as Gimmy is considered too young to be sexualized.) 
  
  
  Scenes added include:
  
  
  Kamina trying to peek at the girls.
  The beastmen fool Kamina into giving up Gurren-by offering to remove the pixellation seemingly covering their nudity. (Of course, they
  aren't actually naked-just wearing tiny, skin-tinted swimsuits.)
  The beastmen using a shock collar-like device on the girls.