"Predict and Expect"
As was mentioned, one distinguishing feature is whether it is an "informed guess" or an "opinion".
Another aspect I'd like to mention is the involvement or interest of the speaker in what's talked about.
"expect" implies something that one seriously thinks will happen, which is of interest to him - it may affect him.
"predict" on the other hand sounds like the speaker is less involved with the outcome, as if observing it as an outsider.
Examples:
- Don't expect me to be your friend. (serious - whether I'm your friend or not is important to "you")
- I predict they will not last long. (not as serious - sounds like there isn't much vested interest)
Here's interesting lines from a song ("Desperadoes Under The Eaves" by Warren Zevon):
"And if California slides into the ocean
Like the mystics and statistics say it will
I predict this motel will be standing until I pay my bill"
He is being sarcastic while talking about an hypothetical, improbable event, so "predict" is better.