The 635 has a better DSP processor, it has an upgrade port, it has one more component video input, it has a better remote, it looks better with the flip-down door on the front (but who cares), and it is obviously more powerful.
The only thing that the 340 has over the 635 is Ipod connection, but who cares about Ipods. When HK releases the 640 and 440 for that matter they will have Ipod connections and a few extra features as well. Go with the 635 it is all around BETTER than the 340 IMO.