Guys c'mon, I've seen thousands of PC's with terrible components last for 10 years, stop nit picking.
But yes, the Gigabyte UD3 is the no-brainer, I was just saying there's not really that much of a difference. And the South Bridge does run hotter on the Asrocks... but, honestly... who cares. If you don't know what a SB is, you shouldn't be building PC's in my eyes, and certainly shouldn't be concerned with these somewhat more advanced issues.
Either way, you'll be happy with the performance, even if you got a Zoostorm PC and stuck an HD 7850 in it... I've had an i3 rig next to mine with an HD 7850, running Call of Duty Black Ops 2/Arma 2, and I can tell you now, you'd have to be a fruit bat to notice the visual/performance difference. The only major difference was my monitor. Switched them round and it looked/felt almost identical, and I'm obsessed with every minor detail of my PC... you have to make your mind up how far you want to go with this build. I can make your mind up for you and build you something that'd do what you asked without any issue, but you won't be satisfied with the result, because you'll want to know all about it, if you're getting best price/performance or whatever.
And I can tell you now, if you want this rig to last your Brother, I'd whack it on Scans finance, get something a little better, but pay the same as you thought, and pay whatever off whenever within the 9 month period. If you can't pay back by then, no worries, you can pay it monthly. Finance to me is a no-brainer, and if anything goes wrong, they treat you like a god, give you brand new components with no questions asked. Scan is brilliant.
Then you could get an i5 3570k, HD 7950/ HD 7970 or a GTX 660ti/ GTX 670, pick a case you actually LIKE, and go for it, pick the parts yourself, with almost no restrictions.