Dead seems more honest and direct to me. People should find comfort in other things instead of pleasant language.
Passed away if I'm breaking the news. Any other time I'll put it as humorously as possible to lighten the mood, unless I get the feeling it really isn't welcome.
Just whatever comes to mind, either dead or passed away. By the way, for all you high school English students, 'passed away' is the most common example of euphemism in the English language.
"It's passed on. This parrot is no more! It has ceased to be! It's expired,and gone to meet it's maker! This is a late parrot! It's a stiff,berrifted life! It rests in peace,if you wouldn't have nailed it to the pearch it would be pushing up the daisies! THIS IS AN EX-PARROT!" But if I would be seruious I would use both,depending the situation.