One major difference which I happen to know that exists between the two is that the earlier model was not capable of handling the 4 Ohm speakers but the newer 405II was improved in a way that it was able to handle 4 Ohm speakers as well.
I remember having read a very interesting article long time back in which the Quad 405 was compared with a Naim amp. Two speakers were used one having 4 Ohm impedence and the other with 8 Ohm impedence.
The Naim sounded terrific with the 4 Ohm speaker but Quad was not sounding good. After this test the speakers were switched and the result was otherwise. Quad with the 8 Ohm speker sounded terrific but not the Naim.
Those who had conducted this test were very surprised at the results as no one was expecting it would turn out that way.
I had a 405II and 34 in pristine condition which I sold to a good friend who is now driving the Rogers LS3/5a's and is very happy. The Rogers as you know are 11 Ohm speakers and they are a piece of cake for the Quad 405II in terms of handling.