"expect...to be" is much more common. It essentially means "require".
"I expect you to be able to do this. If you can't do it, I will fire you."
"expect...are" is much less common. I almost never use it in American English, but I see it occasionally in British English. It essentially means "believe" or "I think that probably...".
"I know that you've done similar jobs in the past, so I expect that you're able to use all the equipment. If you see any equipment that you aren't familiar with, feel free to ask about it, and I'll show you how to use it."
"expect" can also mean "predict". For this meaning, you can use either a "to" pattern or an "is verbing" poattern. In America, the "to" pattern is much more common. I'm not sure, but I think that in England the two patterns might be close to equally common.
"He didn't tell me exactly when he would arrive, but I expect him to arrive soon."
"He didn't tell me exactly when he would arrive, but I expect that he's arriving soon."