First up, the soap made with water. The lather has increased quite dramatically. It lathered easily and the bubbles are both creamy and bubbly.
Then, the soap made with apple cider vinegar. Again, it lathered easily and quickly. It doesn't look like as much lather but it felt amazing... silky, creamy, luxurious. I much preferred the lather of the acv soap to the water soap. Both bars are nice and hard but the soap with acv feels harder to me. I can't back that up with any definitive tests, just what I could feel. Both bars have a lovely waxy feel to them and, at this point, both are lovely soaps.
I'm kind of biased towards the cider vinegar soap at this point. I'll try both again this weekend and have John take more pictures. I think, at this point, I can safely say that the cider vinegar experiment has shown that it makes a really nice soap. I know, from online reading, that using vinegar will up the superfat and that probably contributes to the creamy feeling but if I want to make a "special" soap, I'll definitely consider making it with apple cider vinegar.