In my experience 4:3 has been easier to handle and I've always used it for most of the photography I do, I'll elaborate on this.
4:3 images can be later made into 16:9 and from my testing I can see pretty much the same whether in 16:9 or 4:3, I choose 4:3 for the extra detail.
But then again I've never had the opportunity to photograph using a 41 Megapixel camera.
In the phones I've owned, the Sony Xperia S, Lumia 520 and the Nexus 5 there is quite a gap between the megapixels you get when you switch between 16:9 and 4:3, plus I've always found it better to frame my shots in 4:3.
For example, here's a landscape I took at 16:9(6 Megapixels):
And here's the same scene that I possibly framed better on 4:3(8 megapixels):
In short, from the phones I've owned and my own personal preference has always been 4:3, I hear it's better for those that print their images as well.