Apple uses a lightweight and flexible wire for connecting their mobile products. This is actually very nice except they won't take much abuse. Cables breaking at the plug is a common problem across the industry. That is why strain reliefs are made. You'll notice that the cable on your other connector is a little heavier and stiffer which will protect it a little more from too much flexing near the plug.
Also, even if the cable doesn't break, there are some other things unique to these cables that can go wrong. I've had several 3rd party cables just stop working (6 in the last 3 years). If I understand correctly those lightning plugs aren't passive. I.e., they don't just connect the wires to the various pins on the connector. There are electronics inside the plug between the wires and the pin connectors. The electronics themselves can go bad.
Which makes me wonder, If one end of one of these cables is plugged into an active device (i.e., turned on), and the exposed pins on the free end of the cable are shorted or gets wet, can this cause the electronics in the plug to be damaged? Is there anyone in the forum here familiar with the guts of the lightning cable plugs that might answer this?