I don't know a great deal about phones (so I'll have to pass on the main content of your question - sorry!) but I do know quite a bit about cameras and I can confidently tell you that you should ignore any 'difference' between 13Mp and 16Mp.
Because it's quite cheap to add extra megapixels, phone and camera manufacturers keep increasing the number they offer in the hope that purchasers will be conned into thinking 'more is better'. It isn't!
Unless you're planning on producing prints bigger than A4 size, you don't need more than 5Mp at the very most. Indeed, even when printed at A4 size, I'd defy most people to be able to tell the difference between an image taken with a 3Mp camera and a 5Mp one. Above that additional megapixels become meaningless. (It's like offering car buyers a model which can go at 1000mph, even though they'll only ever drive it on public roads and within the legal speed limits. The extra speed is completely pointless).
I've even seen it argued (on well-respected websites and in equally well-respected technology magazines) that trying to squeeze a vast number of megapixels onto the tiny light-sensing chip in a phone camera can actually lower image quality. (Top-of-the-range professional DSLR cameras might offer plenty of megapixels but they'll also contain a far larger chip for the image to be focussed upon).
All that having extra megapixels in a phone camera does is to produce larger file sizes, taking up far more of the precious memory which you're concerned about.
You might well see reviews stating that phone A takes far better pictures than phone B and I'm not seeking to rubbish such reviews. However the difference will be down to the quality of the LENSES in those phones, rather than having anything to do with the number of megapixels the phone cameras have got.
If you want really good pictures, buy a proper camera. The lenses in phone cameras are too small to allow enough light in for good quality pictures in all but the brightest of conditions. They try to compensate through using slow shutter speeds but that produces a high risk of ending up with 'camera shake'.
However if you're determined to stick with the cameras in mobile phones, read the reviews of those phones carefully to see produces the best pictures (because of a higher quality lens) and IGNORE the number of megapixels.