P&s come in all levels of quality, at all prices. If you took the iPhone 5 and stripped out everything completely unrelated to photography, it would be a $200 ultra compact p&s.
There are certainly p&s cameras that are better, but there are also many that are inferior. IMHO, the iPhone 5 kicks the pants off any p&s under about $150.
What's the value of a p&s that has a high quality f2.4 lens, 8mp camera. With built in GPS, built in wifi sharing, touch screen focus, hd video, and high quality in-camera photo editing.
The only thing you miss is optical zoom. Then again, the Sony Rx1 is the best "p&s" there is... And costs $2800, and it doesn't have optical zoom either. So the iPhone 5 is in good company in this respect.
So to me, the question is whether (1), you already own a super high quality smartphone camera and (2), are you looking at p&s cameras that are actually better.
I wouldn't spend $100 on a run of the mill p&s, just to have something apart from my iPhone.
Anyway, to see the ability of the iPhone camera, here is a link to a professional photographer who took her iPhone on an around the world trip.
http://mostlylisa.com/worldtrip/
In reference to the OP.... If she got something like the Canon S95/100/110 which is in that price range, I do think that camera is quite a bit better than an iphone.