Well I can't tell you exactly how different they perform, but this should give you a general idea of what fps you "could" get
http://anandtech.com/bench/product/776?vs=778
it looks like crysis is the only game on that list that you play unless you meant crysis 3, but anyway im sure it will give you an estimate on the difference in the 2 cards, an 7850 is definitely better. It's good that you could lower the 2TB drive down, i figured you needed that much space for something like movies you had so I left it alone.
Here is a build that is at your max budget, you get an i5, an HD 7850, and a slightly better motherboard
PCPartPicker part list:
http://au.pcpartpicker.com/p/2gke5
Price breakdown by merchant:
http://au.pcpartpicker.com/p/2gke5/by_merchant/
Benchmarks:
http://au.pcpartpicker.com/p/2gke5/benchmarks/
CPU: Intel Core i5-4570 3.2GHz Quad-Core Processor ($222.00 @ CPL Online)
Motherboard: ASRock Z87 Pro4 ATX LGA1150 Motherboard ($130.00 @ CPL Online)
Memory: GeIL EVO Leggara Series 8GB (2 x 4GB) DDR3-1866 Memory ($95.00 @ Scorptec)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($67.00 @ PLE Computers)
Video Card: XFX Radeon HD 7850 2GB Video Card ($175.00 @ PCCaseGear)
Case: Cooler Master K380 ATX Mid Tower Case ($54.00 @ CPL Online)
Power Supply: Antec High Current Gamer 520W 80+ Bronze Certified ATX Power Supply ($85.00 @ CPL Online)
Optical Drive: LG GH24NSB0 DVD/CD Writer ($22.00 @ Mwave Australia)
Total: $850.00
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2013-12-07 16:36 EST+1100)
Now I'd like so say that's all, but from what I've noticed I haven't seen a single thing require some kind of shipping so I'm wondering if pcpartpicker doesn't have an estimate on what shipping would cost in Australia. so if that's true you could be way over budget if you add the cost of taxes and shipping
If it is you could try lowering to an i5 4440, its cheaper, the only reason I chose the 4570 was because it has a higher boost clock at 3.6 Ghz and the 4440 is 3.3 ghz but its up to you if that extra power is worth $17. you can also move down to the 7790 if you need to save money you can refer back to that link up top to see what you would be losing gaming wise. and lastly another way to save money is to get a different motherboard, either an h87 or just a cheaper z87 if you'd like, the z87 is in the more performance and gaming side of the motherboards while the h87 is like your normal everyday kind of one but if you're on a budget it could work for you