5 or 6 years ago I would always book through Priceline, Expedia, Orbitz, Hotels.com, etc. for flights and/or hotels and the prices were almost always better than going directly through the airlines or the hotels.
The past few years I've ALWAYS found the same or better prices by going directly to the hotel or airline. When my wife and I went to Florida last month, the airfare was about $150 cheaper (even after adding in all the fees) per person through Delta.com than it was through Priceline and the hotel we stayed at for a few nights was also cheaper than (and nicer) than any of the similar ones coming up on the travel websites.
Even when the price works out the same, at least by booking directly through the airline or hotel I am guaranteed that I can add up my rewards points or frequent flyer miles.