There is no question that Altman has been and is huge inspiration to PTA. In that regard comparing any work of Altman to Anderson doesn't seem artificial to me.
"Magnolia" was the first film of PTA I have seen. Since then I re-watched it again somewhere between "CMBB" and "Master", so my memories aren't fresh. Maybe it is time to revisit it?
Anyway "Magnolia" feels much formal to me than "Short Cuts". Opening of "Magnolia" is good example of that. It set ups mood and themes in the beginning of the film, in your face way. On the other hand "Short Cuts" are more subliminal (probably same goes for other Altman). There is voyeuristic feel to it - we got glimpses at lives of characters, often without much explanation to their behavior, film is resolved without conclusion.
Compared to that PTA is much more attached to characters, he cares a lot more for them. Cop character is good example of that - in both films they are stupid, but in case of PTA there is true sense of calling and that makes him much more likable.
Themes are also more visible in "Magnolia", maybe even to the point of being sometimes repetitive. In case of "Short Cuts" it is easier to point out themes after seeing the film than in the middle of watching.
Not sure if this is helpful at all, since I compared those films in very abstract way.