I'm with the majority---the 4s is significantly quicker (at almost everything) than the '4'. We set our son up with the 4, sim-less, as his iTouch. Works well, but is starting to show it's age with different games that have no issues on my wife's 4s. Regardless, all of our phones are on iOS6 so the idea that she won't be updating to iOS7 isn't relevant.
Does the 4 still work? Yep....and will continue to do so as a talk/text device for some time I'm sure. But the 4s's guts were completely updated and hence future application updates...who knows, maybe she DOES get into Facebook, Twitter....or Betty Crocker's cook everything app---in a couple days time, the 4s, if still held around and kept as the 'dollar' model will be a much better investment for her, regardless of how 'tech savvy' she is. The camera is also much improved...and we ALL love to have a decent camera on our phones, as it's always with us---Moms included
We're just way too close to the event announcing new iPhones, including the '5c' which again....regardless of how savvy you consider your mother, may very well enjoy it's color choices, LTE speed if she's using the internet at all on the run, the ability to run the latest apps and OS---and at possibly a lower, $99 entry price...it could be an excellent choice that WILL indeed be relevant for a few years. The other factor is connecting devices....and the latest Lightning connector....anyway, just thinkin----regardless of what you choose, you WILL be paying the subsidized phone charges within your monthly bill. In the US, the choice of phone is irrelevant, the monthly charges are the same. This being the case, why NOT get something that IS current and isn't going to be handicapped moving forward?
I guess I don't understand why you would consider the 4. The 4s is definitely, performance-wise, a big step up from the original regardless of what some will tell you (see anandtech.com for the actual differences and a well written review)
Good Luck!
J