The green batten are the "old" stiff battens. My boat runs a mixed set with green ones up to the top 4, which are the newer white ones. The difference is just as you stated, green = stiff, white = softer. The white ones come in several flavors... stiff, med, soft... ect. The soft ones are really too soft for the most part. I think w/o doing any research, the current set up is mostly med white battens.
For purposes of tuning, owning a set of both would probably be a good idea. Use the green when it is really blowing and the white ones for when it is not.
Will R.