The precision will have the tone it sounds like she is looking for, so if her hands can deal with the precision, that's the route I would suggest.
The necks are different on the basses, the p neck is thicker than the j. You said she has "adult hands", but that doesn't mean she'll necessarily want the bigger neck. The jazz will also probably weigh a little bit more.
I'm 95% certain the Precision Deluxe he's talking about has a Jazz-spec'd neck.
@Revpatn; If you can, take your daughter to a local music store to let her get a feel, not to mention an earful, for what a basic Precision and Jazz have to offer. But, like I said before, I suspect that Deluxe will have a Jazz-style neck, so the big difference between it and the Geddy-signature Jazz will be it's front-to-back thickness. Geddy-sigs are known for having some of the thinnest necks in the Fender family.
Other basic differences between them are the sounds…Precisions tend to be "boomy", Jazzes lean towards "growly", especially ones with what's known as "seventies-era pickup spacing" which accentuates that growl even more. The big questions are, "Which sound does she like more?" and "Which feel better in her hands?"
Ultimately, if both instruments are in good working order, either will be a good platform for her introduction to "The Low End".
Oh, and be sure to ask anyone selling a used instrument when the last time it had a decent setup. If it's been a while, you should be ready to give your pick a proper, pro-level setup and maybe a new set of strings. It was the first thing I did when I got my first bass and I'm very glad for it. Being told mine was in excellent condition, outside of some minor adjustments and a few chips in the finish (so-not a big deal!), was a tremendous weight taken off my mind.
The strings the music shop guy suggested also helped too. He set me up with a set of D'Addario Chromes .100-gauge flatwound strings. They sounded great on my bass (a P/J bass, no less
Good luck, happy hunting and please keep us informed as to what you eventually find for her first-ever bass!
