I am a very huge Janis fan too, and I know this song very well (I think it's great, by the way). I wouldn't say Big Brother tried to imitate Airplane! I love Big Brother's music as well as Airplane's, and I think the two bands played diffferent kinds of music (moreover, I would say that Big Brother was less proffessional than Airplane).
In my opinion Big Brother's music is less psychedelic than Jefferson's - that's why one of their most psychedelic songs - 'Light Is Faster Than Sound' -may sound like Airplane. But no, never will I agree that they tried to imitate Airplane. As it has already been written, most of the San Franciscan bands at the time tried to become as psychedelic as they could.
And Big Brother, I think, is a really original band with it's own music style!
If you smile at me
You know I will understand
'Cause this is something everybody everywhere
Does in the same language