If I have to choose between the two I would go with buy a new PC. Even though assembling a PC sounds like a great idea there are sometimes faulty parts that get through quality control and if you happen to get one of those parts the assumption of the manufacturer is YOU did something wrong and it is a fight to convince them otherwise and then often the manufacturer will blame some other part for not working when they learn you are assembling a computer. Buying a new computer just avoids all those potential issues dealing with part manufactures and has a simple warranty.
I go with a third option though. The last three computers I've bought were refurbished which is almost like brand new but much cheaper.