Well... It is probably said that way because some phones, like the Lumia 520 for instance, get 16:9 pictures by cropping out of 4:3 pictures. This means that the sensor is less utilized compared to in Lumia 830. The below diagram is for the Lumia 920, but it should be the same as the 830.
Whereas on the Lumia 520, images are obtained as below:

Blue:4:3.... Red: 16:9
Now, compare the 16:9 images on both phones:

Orange: 16:9 on Lumia 920 and 830
Red: 16:9 on Lumia 520
Here you can see that itis significantly bigger on the 920 and 830.
But let's go back to the first picture. If measured, the 4:3 still measures larger area than the 16:9. To get maximum quadrilateral area in a confined circle, the closer you are to a square, the larger your area.
So to sum this up, use whichever you like on your 830. But I use the 520, so I'll stick to 4:3, since 16:9's are essentially cropped 4:3's.