Which camera gives more accurate image, the front or the back camera? My phone is Kyocera Hydro Icon with Android 4.4.2. 

I use its back and front cameras to take pictures of my head and face at distances around an arm's length. I found the front camera gives more pleasing pictures than the back one, for example,
the pictures taken by the back one often shows my eyes are proportionally smaller.  

Also the front camera seems to produce completely dark pictures when the lighting isn't good, while the back camera can still produce clearer pictures.

Which camera gives more accurate or realistic pictures of my face and head at distances around an arm's length?
Resolution governs quality of pictures


The back camera invariably is of higher resolution and is meant for better quality. Typical resolution is upwards of 10 Megapixels
Front camera is not meant for high resolution and was intended for visiting the image during video chats. With demand for better quality (including "selfies", it is now typically upwards of 2 megapixels and in recent phones 5 or more. Dark images as reported is less for to quality of  camera but more to do with subject focus and lighting conditions


Edit

OPs concern is more about "distortion". To reduce distortion 


Take the snap at arms length, picture would be smaller but less distortion
Reduce aspect ratio (if default is higher) to 4:3
Keeping the subject and camera at same level and experiment with aligning your face to the top/bottom edge of photo to see if it reduces distortion
Try an app like Cameringo, which augments photo taking capabilities considerably and adding effects (I use the pro version of this but more for rear camera shots and both trial and pro versions are good). This may also help tackle the rear camera issues faced