It's believed that Canon puts Sony sensors in some of their compacts, and that some X-Trans sensors are actually manufactured by Sony as well. Panasonic makes the current m4/3 sensors for both companies, and they compete well with Sony's offerings.
As for the Leica T vs. the A6000, well, it's only a fair comparison if you search out the very best glass for the Sony camera. Their kit lenses are trash, might as well be marked 'toy' lenses compared to similar designs from Fuji, Canon, or Nikon, and yet those all pale in comparison to what Leica built for the T. Think of Leica's 18-56 lens as a modern range-finder-sized Canikon 24-70/2.8 optically. Being slow keeps it small, and that's okay; it's an amazing optic.
I compare the Leica T more to the EOS-M than anything else; they created a small, simple, well-built camera with a great touch interface that can be adapted to use the best glass on the market, in Leica's case the M-mount lenses, and likely R-series and S-series as well. And like the EOS-M, the T-series is a great introductory camera with great initial lenses that needs to be refreshed with a better sensor and a slightly more refined body with better manual controls in order to come into it's own, but the potential of course is there!
To call all of the Sony E-mount lenses trash is a bit of a harsh generalization. Yes, most of the cheaper ones are (but there are a couple decent ones). And most of the more expensive Zeiss lenses are pretty good. Yes, perhaps not as good value in optical quality for the buck as Canon, etc, but then we're comparing to Leica here (which is rarely a value proposition). And of course, you can use those Leica lenses (as well as the canon, 1/3 the cost, etc) on the Sony with adapters...
Edit: woops. You said kit lenses are trash. Fair enough. I thought you said all E-mount lenses. Reading fail. The fact of the matter is that the a6000 is such a better value proposition (better sensor, better functionality, EVF, etc) for the body insofar as what you can get out of the camera, that I think the lens situation would be more than worth the trade-off for most.