CTEs, range types, window functions, custom aggregates, functional indexes, conditional indexes, proper utf-8 support and once you bring Postgres with its unique features into the mix: kick-ass JSON support (including the usage of indexes), array support (any my best friend array_agg())

Regarding corruption, it's an anecdote, but my girlfriend has lost a ton of data for her thesis related to innodb corruption. It took me hours of bit-twiddling to get the data back (and into Postgres where it's safe and accessible since then - on the same hardware, so don't blame this to broken hardware)

Now I can totally accept that this might have been a one-time fluke, but I personally really have trouble trusting a DBMS once it has lost data due to causes other than user-error or hardware faults.