Off the top of my head, The Empire Strikes Back is the only example in any genre where a sequel surpasses the original (I'm sure there must be others, but I am also sure they are few and far between). There are probably many good reasons for this: the creative process is not infinite and must run out of steam; if the original is a great success, it sets expectations far higher than it can deliver; and simply, that we get bored of exactly the same thing over again, yet a sequel must stick to substantially the same material and themes as its predecessor.
Given the uphill struggle it faces, Tears of the Giraffe fares quite well, though I do not think it is quite up to the surprisingly enjoyable The No 1 Ladies' Detective Agency. The first book was very episodic, almost a short story collection with some parallel processing, whereas this book, for the most part, has a smaller number of plots. There is also rather less detecting. The characters are still charming, whether it is Mma Ramotswe's reflections on heaven and hell ("perhaps a bit like Nigeria, she thought"), Mr J L B Matekoni's honesty and fecklessness at the orphan farm, or Mma Makutsi's first case as Assistant Detective (and Secretary).
Mma Ramotswe's main case in this book concerns the disappearance of an American man from a commune on the edge of the Kalahari desert a decade earlier, but she also has to contend with her fiancé, his (too) charitable nature, and his dishonest maid, while also concerning herself with the ambitions of her secretary and the ethical dilemmas involved in her work.
Though this and the earlier book were brought to life quite well a month or two ago in a mini-series of The Afternoon Play on Radio 4, the editing increased through the episodes, and there are more details where the book differs from the play. I enjoyed listening to the plays on the radio, and hope that brought about a wider audience for the books, but I have to say that the books are definitely superior. I have plenty else on my reading list for now, but I'm looking forward to the further books in this series at some point in the future.