Is there such a thing as an actual 60W draw LED or CFL bulb?
Yes, you're looking for lights with a high lumen output.  Since LED/CFL bulbs don't convert heat to light, the wattage isn't directly proportional to the light output.  As an extreme example, consider that a 2 watt laser is powerful enough to burn some materials, or blind you!

What you'll likely find is that more expensive LED bulbs from lighting specialty stores are brighter than the cheap bulbs you find at your local home improvement store.  

There are other characteristics of the bulb other than power which impact the perceived brightness - reflectors are a good example.  A bulb with a wide spread will seem less bright (in a room) than a bulb with a narrow spread since the light is being diffused more.