It depends on what exactly is in the laptop and the desktop.
Computer performance is made up of many components. A CPU that is truly equal will perform equally. In general, laptop hard drives are slower and laptops are built with lesser graphics chipsets. However, that doesn't mean a high end "desktop replacement" class laptop couldn't easily outperform a value segment PC.
High performance and mobility are conflicting goals. Laptops that perform comparably to the upper end of desktop computers (
example) tend to be large and heavy, and have poor battery life. They are suitable for limited mobility applications, when you don't intend to carry it with you daily, but need to move it more often than you would care to move a desktop computer. You will pay more than you would for a comparable desktop.
If you want something small and light (
example), suitable for taking everywhere, with great battery life, then you should prepare to compromise on performance and still pay a lot.
Cheap laptops are neither fast nor small. Quite frankly, they are crap.
