I've used a lot of shorties, and in the last years I settled with two Hofner (reissue 61 and reissue 62) and a Mustang JMJ. I love them, and never ever had problems with the sound.
I've used the Mustang even with roundwound strings in the past (I've had two Japan (crappy instruments... can't undestand al the fuss) and a Vintera), and always sounded perfectly, in particular playing in a mix.
I've also had a couple of Danelectro Longhorn, totally different sound, they are thin and middy, and played for years with two Ibanez Mikro (one with rounds, one with flats), and they sounded like any long scale PJ I've ever had.
also a couple of Gibson SG (again, rounds and flats) I've used on a lot of gigs and recordings for three years straight.
IMHO the real thing about short scale basses is that the vast majority of models are "60's projects" (hollow, semi-hollow, SG, Mustang...), and they were all designed to have different sounds compared to the long scales.
an SG won't sound like a Precision/Jazz, it's not designed that way, as for an Hofner.
the Mustang is similar to a Precision, and you can hear the differences mostly playing alone, but in a band mix it's difficult to tell them apart, and the Mustang is so easy to mix!
the Ibanez, even with a 28.75" scale length, sounded full and complete, like any other "big" bass, and even had a perfect slap sound with both pickups on.
I've gigged the Mikro a lot because of the super light weight and extreme comfort (it's like having a necklace, not an instrument

), and never complained about the sound.
the fun thing is that every time I gigged one of those Ibanez, both bands and soundguys told me that they didn't expect that sound from a bass so small.
I love shorties
