There are issues with both groups;

Di2:
-total power failure (broken/damaged cable).
-crash damage can damage the servo motor in the rear derailleur.
-you have to charge the bike infrequently (the horror!)

Cable-operated:
-total failure (cable can snap at the right radius bend in the shifter--a common issues with recent generations of STI shifters).
-crash damage can render the rear derailleur inoperative.
-you have to change the cables/housing infrequently (the horror!)

And so on... The point being that the differences are best left to personal taste, rather than reliability:

-some riders don't like the indistinct feel of shifting Di2--"clicking a mouse".
-cost to replace components, if they break (Di2 being more expensive, all else equal).
-satellite shifting options (Di2 only), or ease of changing handlebar configuration (shifters on aero bar extensions...).

You'll notice that I didn't include batteries dying on a ride...because you really need to ignore the system for it to happen. The junction box will flash a number of shifts before the front derailleur (the power hog of the system) is shut off, allowing you time to shift to an appropriate chainring to get home; the rear derailleur is still powered for a time afterwards, allowing you time to plug in when you make it home.