Asus ROG G73JH laptop vs. mini-ITX build

As it stands it's definitely better than your laptop, by a comfortable margin.
There are however, a few things you should perhaps consider. I'd personally use the more modern socket 1150. It's not really more expensive, and has quite a few extra features which make it better value overall. If you need Wifi, it's probably worth getting integrated Wifi on the motherboard, though this will cost you.
For memory, hunt around for the best deal whenever you come to buy, memory is the worst culprit for prices bouncing around and you can save quite a lot by shopping around.
The PSU has a few issues. Firstly your graphics card requires two PCIe power cables, and it only has one. You can use adaptors, but this isn't ideal for a variety of reasons, especially in a compact case. Secondly, while a 430W PSU is sufficient for this setup, it makes sense to go a bit higher as it gives you more flexibility with upgrades - a 550W PSU will basically power any standard graphics card you could want. Thirdly, the Corsair CX range are fairly basic. They offer good value for money (at $30 it's unbeatable really) but they aren't the greatest quality. If you are really struggling for funds, they can be a decent option, but I'd suggest ditching the SSD rather than going cheap here. Finally, the layout of the case puts the PSU on top of the motherboard, meaning cables will hang down. This means that a modular/semi modular PSU is highly desirable here (when in for example, a Bitfenix Prodigy, it's not that big a deal) but finding a quality semi modular PSU for less than say $70-80 is very challenging. The PSU I included is total overkill, but it's a great price for a great unit, and pretty much unbeatable (it's already sold out at Newegg).


So here's my suggestion with those considerations -
PCPartPicker part list / Price breakdown by merchant / Benchmarks

CPU: Intel Core i5-4440 3.1GHz Quad-Core Processor ($174.99 @ SuperBiiz)
Motherboard: MSI H81I Mini ITX LGA1150 Motherboard ($67.30 @ Mwave)
Memory: G.Skill Ares Series 8GB (2 x 4GB) DDR3-1600 Memory ($64.99 @ Newegg)
Storage: Crucial M500 120GB 2.5" Solid State Disk ($69.99 @ SuperBiiz)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($59.23 @ OutletPC)
Video Card: Gigabyte GeForce GTX 760 2GB Video Card ($249.99 @ NCIX US)
Case: Cooler Master Elite 130 Mini ITX Tower Case ($44.99 @ Mwave)
Power Supply: Antec High Current Gamer 620W 80+ Bronze Certified Semi-Modular ATX Power Supply ($59.99 @ NCIX US)
Optical Drive: LG UH12NS30 Blu-Ray Reader, DVD/CD Writer ($47.27 @ TigerDirect)
Total: $838.74
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2014-03-23 20:55 EDT-0400)
It's $30 more expensive, but that comes all from the PSU. Normally I'd suggest the XFX-550 for $45, which is again, great value for a great unit, but I feel like right now the Antec is the better deal, and more suited to this build.
You also get modern motherboard features like SATA6, PCIe3.0, USB3.0 and quite a lot of other stuff. Additionally, while the 3350P is a great value prospect, I'm loathed to recommend it for ITX builds. With no IGP, it removes the option for you to convert a build like this to a full HTPC type setup somewhere down the line (for which you don't need a graphics card). Additionally, the 4440 is faster (slightly) and cheaper, so it's a pretty clear winner.

One thing you didn't mention was your display resolution. Assuming you are running a 1080P display this is a very solid setup for playing modern games right now, with the capability to run at maximum or near to maximum settings.