I've had the ii versions of both the 1.4 and 2x converters for many years. While I generally use them only on longer lenses, especially my 300/2.8, I have also put them on the 70-200.
While I haven't tried it yet, I'm inclined to go along with the view of others here, in that the 1.4x iii is only a very slight improvement in terms of IQ over the ii. The results I've had with the ii are excellent matched with my 300, and very good on the 70-200 (both the original and ii versions of the 2.8 IS, as well as the 4 model).
On the other hand, the 2x ii with the 300 was only fair to good, and absolutely terrible with the 70-200 (the earlier 2.8 IS, anyway). It became much better with version iii, though still not at the same level of the 1.4x. If you ever consider buying a 2x, it's money well spent getting the latest edition.