This was a test with a Sigma 10-20mm DX lens on a Nikon D800 (FX) body compared to a Sigma 14mm FX lens on same body. The first shot is the 10-20mm DX lens shot in FX mode (default). The second shot is the same 10-20mm DX lens with a 1.4 Tele-converter added shot in FX mode. The third shot is the 14mm FX prime lens shot in FX mode.
Using a 1.4 Tele-converter on the 10-20mm DX lens results in a wide angle shot almost equal to the 14mm FX prime. It's actually a little wider than the 14mm... closer to 12mm.
Originals Available at: www.geneinman.com/nikon_d800