This article is from the Chihuahua Breed FAQ, by firstname.lastname@example.org (Melinda 'Bob' Casino) with numerous contributions by others.
I am told that there is no difference in personality, only in the
amount of time you'll spend grooming and cleaning up after the dog.
Long-hairs can shed alot; and they'll need regular brushing. Their
bib (the furry part of the chest) can get dirty and matted.
Additionally, long-hairs can occasionally get fecal matter stuck on
their "pants" which will require snipping off. As for bathing, the
long-hairs will need it more frequently, and it'll be a longer
process (washing & drying).
Some Chihuahua owners swear by long-hairs and wouldn't have anything
else; it is as much a matter of personal preference as coat color.