as a rule of thumb I would keep only what you need as a minimum in the bank and the rest keep in 'your control'. that may mean a safety deposit box or a treasure map...
but both usually are safer than keeping it in the bank itself.
as many have said above, the higher rate, the higher the risk.
was not so long ago (2001) that they were offering HUGE savings rates and many locals and expats rushed to put their money even in 'safe' US named banks here in Argentina.
When the crisis hit, they devalued the currency, froze your assets and said, "Discúlpame"...