Hard to compare without knowing case, PSU, graphics card (1st PC, card is about £130). Processor is about same price. DDR3 memory in first machine, about 50% more expensive. Operating system kosher or dodgy copy (£80ish if not dodgy)? Etc etc. It's possible to put a machine together for that price, but performance would be down compared to the first.
I build my own

. But not really a PC gamer, so do them for about £500 and get something reasonably performant without being silly money. 6Gb memory not really that useful unless you're running lots of apps at once. And unless he puts a 64bit OS on there, you may as well throw 3 of the 6 down the pan.