Haven't read either Kilo-5 book, but I got the gist of them on Bungie's old Universe forum.
And this does in fact pick up where 3 left off, mostly. There's the aforementioned Kilo-5 lore in between, but strictly from a game canon perspective, it's a direct sequel. Rare for a Halo game, actually. Considering that 1 > 2 didn't do it and neither did 2 > 3.
It's certainly better when it comes to eye-candy. Some of the new maps in SpOps are breathtaking. Halo 3 had good environments, but 4 really is a step above. More akin to Halo 2's skyboxes (Dreadnaught in High Charity, the Control Room, etc)
I'll be in my bunk... One does not simply walk into Skuldafn.