What's odd about Borges's Personal Anthology is how boring it is relative to his collected works. Borges explains in a preface that he's left out stories that were "superficial exercises in local color" (or something like that); what remain are bland and repetitive statements of certain metaphysical positions -- about infinity and idealism and such -- that obviously meant a great deal to Borges but are trite as philosophy. A good example of the sort of thing Borges seems to have liked in later life is "The Other Tiger"; for all I know it's a good poem in Spanish but in translation one finds it drab and obvious. A good example of the sort of thing he did not like is "Tlon, Uqbar, Orbis Tertius."
I wonder if this is due in part to Borges (mistakenly) comparing himself to Kafka. Jonathan Mayhew has a delightful post likening the Oxfordian theory of Shakespeare to a story by Borges or James or Kafka. I would be much more specific: such a story would have been at home among Borges's Ficciones but has very little to do with Kafka. I am not sure, either, that a reader who knew Borges exclusively through the Personal Anthology would have perceived the accuracy of this comparison, as none of the "notes on imaginary books" are in it. It seems to me quite inaccurate to bracket Kafka with Borges at all. Kafka's novels can be understood in textbook modernist terms, as being rather like Macbeth -- successful attempts to find objective correlatives for a certain set of feelings, a certain sense the isolated mind has of its relation to the world. This will not work with Borges as the stories aren't mood-driven. A Kafkaesque situation is a nightmare; a Borgesian situation is an artifact.
The Borges stories I like best (other than the enjoyable but silly stuff in A Universal History of Iniquity) are the notes on imaginary books and two later stories, "The South" and "Averroes' Search," which come off for reasons that might be fortuitous. The general problem with writing "philosophical" literature, as Eliot remarks, is that the philosophy has to be realized -- fleshed out, peopled, colonized -- for the enterprise to work. (One should make an exception for purely frivolous uses, like the Hitchhiker's Guide.) A lot of Borges stories, like "The Circular Ruins," are bad b'se insufficiently real. In later work like "The Aleph," concreteness coexists uncomfortably with philosophical notions, but the philosophy comes off as an exotic and unjustified plot device. But in Tlon, "Pierre Menard" etc., idealism finds an odd but satisfying local habitation in names. Like Swinburne's poems (insert more Eliot here) these stories seem to indicate that there are other worlds than the physical one that are rich and irregular enough to "inhabit" or "realize" ideas in: the world of words and literature, in particular. I wonder, though, if the truth isn't simpler: these stories depend for effect largely on the ability of language to refract ordinary objects, say the moon, "into something rich and strange" -- all literature does, I think -- and lose their charm when there aren't any objects to be looked at. I've expressed vaguely similar sentiments about Stevens in the past, the good bits of his poems are the half-distinct, dazzling images seen out of the corner of the eye, while he's going on about something or other. This is probably a somewhat heretical opinion.