Throne is still as bad as I remembered. The first half of the book is a Rube Goldberg plot that eventually will deliver a minor macguffin to where it can provide a source of exposition in the second half of the book, along with a lot of discussion of interspecies sex. Meanwhile, the nominal hero of the book, Louis Wu, merely watches the events from afar. He's interested because the characters he's watching are dealing with the consequences of his tampering with their local environment in The Ringworld Engineers. They achieve a victory, and that's pretty much the last we see of them, except for a few who accompany the macguffin to the hills of exposition. The second half shifts the focus back to Wu, and is interesting for a little while as two rival gangs vie for control of Ringworld, but then becomes more Louis watching what's going on elsewhere until he finally pulls a rabbit out of his hat to defeat the nominal villain, the end. Not terribly exciting at all.
Children turns out to be a much more fun book. Niven goes back to what he's best at - describing the VERY BIG THING that is Ringworld by having Louis Wu physically explore it. (For those not familiar with the series, the Ringworld is a narrow slice of a Dyson sphere rotating around a star. It's a million miles wide, 600 million miles in circumference, and has the surface area of three million Earths.) The villain this time is external. A war is raging among several of the races from Known Space in the space surrounding Ringworld over who shall control it, and collateral damage is starting to threaten the existence of the artifact. The main weakness of the book is that it pretty much assumes a working knowledge of Niven's entire Known Space series, not just the earlier Ringworld books. There's some exposition, but you need to have read the Beowulf Shaeffer stories and Protector to fully understand what the hell is going on. There are a number of retcons, and he ties up a number of loose ends. If you've done all the background reading, then this is a pretty satisfactory end to the series.
My current books are the original Ringworld, because it has been a very long time since I read it, and a Chandler collection, Trouble Is My Business.