I'm leaning toward full frame for the better ISO results. Are there any areas where the D600 is better than the D7000 and vice versa?
better low light/ISO as you mention.
I think upgrading from a d40 to anything modern would be a gigantic jump (I had a d70 at one time).
The d600 is heavier and slightly larger than the d7x00. For the first time last weekend my right finger actually started hurting from the weight with a 80-200/2.8 lens. My finger hasn't complained all year until then. But then, the 80-200 is a large lens.
There's ton of stuff on the internet of d7000 v d600 .. d7100 v d600 etc you can read alot about what people like and don't like.
For me, I really like the photos from the d600. But I also know my camera technique all the way to my post processing has significantly improved in the last 2 years.
The fullframe also resolved a couple issues I had
1 - my basement wasn't big enough for home style portraiture with an 85mm lens and crop . ... I could not take another step back
2 - I really wanted a FF camera - as I had bought all FF lens after my kit d7000. I really wanted to play with Ultra Wide Angle lenses and just a couple weeks I finally ventured out to a car show and did my first shots using my UWA and really enjoyed it. Of course, you can get good UWAs for a crop camera, but I was looking at the nikon 14-24 and it cost more than the d600 body ... so I just made the jump to FF and settled on a 18-35 lens which was inexpensive.
fps is faster on the d7000 than the d600
for the most part the d600 is slightly newer same features as the d7000 and I feel at home on both of them.
d7000 low ISO is 100, d600 base of ISO of 100 but can go to 50. and being FF it gains an advantage of that I think even at 100.
but basically, if you have the money it will be a gigantic step forward.
but then ....
Why the Nikon D600 is NOT a logical upgrade for DX shooters - In The Picture
of course a used d7000 body is $600ish USD and a d600 is still $1200+ ish