For my part, its not a question if a 5150/5350 can run the game, it should do that fine. I just feel you get a lot more value with one of the big core Trinity/Richland/Kaveri APUs for desktop and HTPC use.
Here (Denmark) the 6400K and 5350 is priced identically. AM1 boards cost a bit less then their FM2+ counterparts, but its nothing that really matters.
You do make a good point. The GPU of the A6 is much stronger and a better choice for gaming. It also depends on his case size.... FM2 boards for itx are usually overpriced -- if he is building an HTPC he might be using a tiny case. AM1 boards are dirt cheap for the ITX form factor... That might be the reason why he was leaning toward socket AM1. If he is building a Micro ATX setup, I probably recommend that he go with FM2 as well.
Yes if the OP really needs the speed increase and if size, noise, and power savings is of little concern it may make sense to spend a little more for the FM2 option.
I own and have built for others' several dual/quad FM2 and AM1 type computers for various purposes. My observation is that provided you pair an SSD with either platform, you won't notice large differences under light loads such as XMBC, streaming, surfing, office tasks etc. In gaming there will be a large advantage with the FM2 over AM1 but both the 5350 and 6400K are still very entry level and should only be used to play with low to medium graphic settings at 720P or lower in modern demanding games.
The AM1 platform does have its merits over the FM2 platform and I have listed below some of the reasons why.
Although a bit more expensive, if you go with the AsRock AM1H-ITX you can power it with a $10-15 dollar 60-90W laptop power brick where it would cost at least double that for a decent standard ATX power supply. With the external power brick setup you have even more flexibility in the type of enclosure you home it in.
The AsRock A1MH also comes with a mPCIe slot which in my case I outfitted with a cheap Intel 5GHz A/C WiFi adapter. These types of ports don't normally come on cheaper motherboards and I don't think you'll find a cheap FM2 board that has one. This saved me from wasting a USB port for an external WiFi adapter which in my experience generally do not perform as well as the internal PCI/PCIe cards.
The memory configuration is more flexible on AM1 due to it being single channel only. With FM2 to get the most out of the APU you will need to use at least two sticks of memory. This may cost you a few bucks more (and uses a little more power) than just needing 1 stick for the AM1 platform.
Depending on what your power costs are you will save you approx $5 - $15 bucks a year if left running constantly (likely scenario given its HTPC duties). Although not much, every bit helps. Typical idle power on an FM2 platform is between 25 - 40 Watts (compared to 10-20 on an AM1) and load power is roughly double these figures (more if you go with Quad instead of Dual CPU FM2). Also the stock AM1 fans are very quiet, basically inaudible from more than a few feet away. This is not true for stock FM2 fans, they can get pretty annoying under load.
So in a nutshell, if you feel the AM1 platform is fast enough for your 7 year old (and will be for a few years anyway) I would recommend you go with it instead of an FM2 system.