Improvements of the iPhone 6 over the iPhone 5s All, 
I have (at work) the choice between a: 


16 GB iPhone 6 (A1586) 
32 GB iPhone 5S (A1457)


I'm concerned about the smaller capacity of the newer phone.  I do usually run out of space on my phone.  

Obviously the screen is bigger on the iPhone 6.  Are there any other notable benefits that would lead me to pick the smaller capacity newer phone, such as: 


Processing power
Hardware features
Software benefits/incompatibilities


Appreciate your thoughts, and understand it's subjective to some.
Size vs features will end up being subjective.  Most notably the CPU in the 5s is the A7 and the 6 contains the A8.  Each generation of processor brings a jump in raw power. from A7 to A8 25% inc in processing and 50% increase in graphics with a 50% Reduction in power consumption due to new manufacturing process.  Each version of the iPhone typically come with better battery life.  However, If these are used then the life of the battery will depend on past treatment.  An iPhone battery will only respond to finite recharges and life diminishes over time and use.

Additionally the camera will always have improvements.  A great read on many iPhone cameras can be found at http://snapsnapsnap.photos/how-does-the-iphone-6-camera-compare-to-previous-iphone-cameras/

Motion sensor capability is about the same.

Finally, both phones will be supported by iOS 11.