A lot of prebuilt computers do not give you much say in the quality of components you pick. Your best bet is showing us a pre-built gaming pc and let's see if we can price something out of better quality in a similar price. I've got to disagree with Phil, and say you absolutely will save money building your own compared to a pre-built machine.
Issues to run into with DIY:
Faulty components- it's not uncommon to get a piece that does not work out of the box, where you have to get a replacement from the manufacturer. My PC was perfect which is uncommon (i believe) to have everything work first go.
User error- a pc is pretty straightforward and relatively easy to set up. However, you run the risk of breaking something yourself... I wouldn't worry about that Lee.
Give us a price range and I will go through Cyber Power, iBuy Power, etc as well as give you a custom parts list.