To answer your question a little bit more accurately: SRAM's indexing mechanism in it's shifters is simpler then shimano's. If you look up their video on how leap-frog technology works you will get an idea. If you somehow manage to hunt down my teardown of an STI shifter you will then be able to compare and understand.

I have had both shifters die on me. Shimano shifters basically grind their internals to dust (Atleast older 9 speed did) a SRAM shifter's lever simply broke on me. It happens. I have crashed with both and they both have come out just fine. The failures in SRAM stuff have occurred because of metal fatigue so there is either some hairline crack or damage to the part and it eventually goes. The Shimano shifters I have seen fail are due to dirt and old grease buildup.

One thing to note is that SRAM shifters and their failure rates have an inversely proportional relationship with their cost. Red stuff seems to fail the least since the quality of the internals is very very high since they mainly use CNCed parts for the shifting mechanism. On the other hand Apex and Rival use forged pot metal parts which have a greater chance of breaking.