I shoot a lot of indoor sports and lots of figure skating -- fast, erratic moving subjects in sometimes challenging light. I went from an XT with a 70-300 f4-5.6 (non-L) to a 60D with a 70-200 f2.8 II. Somewhere, in between, I borrowed a 70-200 f2.8 Mark I for my XT and saw a huge improvement. But, noise at 1600 was still noise. With that one experience, I was sold on the 70-200 L. But, I also realized that sensors do matter. It's not like 40 years ago when Kodachrome 64 was just as good in a Canon FTb as it was in the F1.
Since then I upgraded to the 7D and my keeper rate went up significantly due to better focus tracking. But, I still needed Noise Ninja or Lightroom to clean up the noise. I often shoot between 1600 and 3200.
Early this year I upgraded to the 5D3 and my image quality increased dramatically. Rarely do I need to clean up noise. Images are sharper and with the bigger pixels, color depth is deeper. For challenging, harsh lighting, I have more flexibility in Lightroom to tone down the highlights and bring out detail in the shadows.
I went through a lot of mind games to convince myself that I would never "need" full frame because I just couldn't see myself spending the money for it. I thought the 7D was the greatest camera made -- until my 5D3 arrived.
Granted, for outdoor stuff, I still get some good use out of the 7D. But, it's a backup body when indoors.
It's easier to invest first in lenses. They often last longer. That 100 f2.0 should be great lens on crop or full frame. (It's still on my wish list.) But, sometimes there's no escaping the benefit of upgrading sensors (even if the body surrounding it isn't top of the line).
So, body or lens? Yes.