How deeply integrated is your wife into the Apple ecosystem? Because if she has a ton of paid apps, or uses iTunes as a music download market, she should stick with Apple, because she will not have those luxuries on Android. However, Android is really the way to go right now assuming there are no big ties to the iPhone in terms of money spent on their digital products. It just offers the greatest customization and functionality out of the current OS's.
If you had to buy today, the iPhone is not the best option. The fact is: the iPhone 5 is just too far behind technologically to demand a $200 on contract price tag right now. However, Apple is likely to have a new iPhone very soon, so if your wife was an iPhone user before, she can avoid the platform switch headaches by just going with the next iPhone when it comes out.
The thing with the S4, is that it has some lag issues. For someone coming from an iPhone, that is just going to be incredibly irritating. And in the current trends of increasing build quality, the S4 just isn't as good.Therefore, I probably wouldn't recommend it, unless camera performance is a big deal to her. Then, the Moto X doesn't stand a chance.
The question is: "does your wife care about tech specs" and guessing from the fact that she was an iPhone user, she probably doesn't fit into that market. If she is a spec junkie and/o tech enthusiast, the HTC one will probably be her best bet. But for a mainstream consumer, the Moto X is probably the better choice. Its always on voice commands and active display are just far more useful to the average consumer than Airview and smartpause on the Galaxy S4, or Zoe on the HTC One. Plus, you get a ton of colors to choose from, and it is being assembled in the USA. And coming from an iPhone, all of these androids will likely seem ginormous and the Moto X is the most compact of the three major android heavyweights.
So my wife's upgrade is coming up, and she is looking to move from an iPhone 4S to the Galaxy S4. I'm looking for opinions on this, as in should she just stick to Apple and go to the iPhone 5. I know it can get biased, but please at least state reasons for your opinions and not just say "OMG, iPhone because Apple is like D Bomb yo". The other phone that I've been hearing about, but there isn't a lot of details on is the Moto X. The new phone coming from Motorola and Google, and is rumored to be coming out Aug. 23.