I believe both are important and both can be developed. Another technique for developing the right side is gesture improvising, which is basically a type of improvising you do where you try to shut down your thinking process and try to use your intuition or "feeling". See [Invalid or Expired Link Removed] for more about gesture improvising and other techniques to help develop your right brain improviser chops.
Another thing I would suggest is to make sure that ALL of your practicing is musical, whether playing scales, arpeggios, etc. Everything that comes out of the instrument should be something musical that you could be inspired to sing. Over on the DB side I have many times read of bassists claiming that the Simandl double bass material is not musical, which I never really understood. Those exercises can ALL be played very musically, IMO.