In reply to Blue Straggler:
Convertor performance is heavily dependent on lens, so check reviews with your lens. They generally perform better on primes than zooms, or at least zooms with a narrower range. Expect AF performance to suffer too.
> Wouldn't a smaller sensor simply give the same result as cropping your image from the 6D?
No, the smaller sensor will have more pixels relative to the area, so you should get higher quality image than simply cropping from the 6D. You'll want a fairly recent, high end body to maintain AF and high ISO performance. There'll not likely be a big difference between using the 6D + 1.4X, but I expect the smaller senor to have the edge. On the other hand the 1.4x will be much cheaper.
The narrower the view the harder it is handle and to tame camera shake, so you'll want decent support too.