There's a reason these phrases are used together. :)
It's important to prepare for the worst. There's great value in critical thinking, in understanding what could go wrong and working to mitigate potential disaster. The currently popular positive-thinking movement ignores this, to the detriment of many people. We do not live in an ideal world, and smart people don't get on a plane without a parachute.
But preparing for the worst isn't the same as expecting the worst. If you've prepared yourself to respond to potential negative outcomes, you can be comfortable knowing that you can handle anything that comes along, and that you've already prevented disaster. In this situation, it's logical to assume that things are going to be fine.
So, hope for the best because you've prepared for the worst. But don't expect the best possible outcome, either. You can be content believing in a good outcome, knowing you've prepared for problems that might arise. People with really high expectations are disappointed a lot.
Since dating is such a popular topic here, I'll use it as an example. If you're going on a first date, you can prepare for the worst (Meet him at the restaurant, have cash in your purse, make sure you cell phone is charged, wear shoes you can run in, don't get drunk), just in case the guy turns out to be a scary dude. But you can also hope for the best (mutual attraction, easy conversation, common goals, a great dinner and a really good movie). But what should you expect? Well, a reasonable expectation is that the food will be pretty good, the movie will be so-so, the conversation will be awkward, and one of you will be more attracted than the other.
The expected outcome is reasonable--that's about how most first dates go for most people--but you've still left room to be surprised by something very grand, and you've prepared yourself for the possibility that it could be awful. No matter how it ends up happening, you'll be ready.