First one will be miles better for gaming. The 750M destroys 840M, and has more dedicated memory. The CPUs are incredibly similar, and CPU performance is less important in games anyway. But battery life may be longer on the second one. If it's more expensive or the same price, go for the first.
Yeah, it's old, but it makes it cheaper. He only wants it for mainly gaming as well, so he could have been done with an FX 4300, but £10 more? I guess even an 8320 is only £25 for, but you can OC it with an Enermax Cooler, or a Cooler Master one.
I would personally recommend a FX 6300. They are hexa-cores, and overclock like crazy if you've got a Cooler Master TX3 or 212 on there. Get an MSI Gaming edition R9 270 or 270x, 8 GB of any RAM, and you could get an SSD and a HDD. Even get a good colour scheme. Plus, if you're will to fill up...