Or is their even a gap between them?
Most reviews I read say the Galaxy is the better phone, bigger screen and more features.
So what will the new 5S have to close this supposed gap?
she uses way more of the features then I do.
I'm mainly interested in using it for music, web / email and text.
But the Galaxy can use a miniSD card for storage for music / videos rather they having to buy a bigger memory phone.
Those points of your post lead me to thing you are looking for a better phone hardware wise. Here are my two cents:
The iPhone 5S will remain with the exact same form factor as the 5, only the internals will change, which will make it faster per se. The build quality on iPhones is far superior to the plastic Galaxy Devices, however, Galaxy devices carry a lot more hardware features than your average iPhone, such as Bigger Screen, miniSD expansion and NFC (and pen input on devices such as the Note series).
On the software side of things the Android ecosystem, from my limited experience with it, is more open as to what you can do with it; dont like the default keyboard?, change it.
But from your post it seems all you want is a device capable of playing your media and reading your mails, the iPhone is excellent at this. Also you mention your daughter using more features than you would, so you have to keep in mind if those features you wont use are worth the switch.
So in conclusion:
1. Keep up with Apple if you want the best build quality and an ecosystem that works for what you want it to do and nothing else.
2.Go android (Galaxy in this case) if you want more hardware features, like NFC and Bigger Screens, and an ecosystem that allows you to be more open with your phone in regards to customization.
Both ecosystems are excellent for mails, media and communications, all you got to do is choose wether the switch is worth it, and wheter you would use all the features of an Android Phone.
IMO Android has turned into a beast, however, for the time being I am keeping on the iPhone side of things, that is, until I find a feature that allures me (there are many, but not any worth switching for) or my contract expires.