Which Build is Better?

Solution

That's probably about as cheap as you can go without making major compromises.

I've lived with a 120GB SSD and will never do so again, particularly when a faster drive with double the capacity can be had for ~$30 more.
You can manage a 120GB SSD if you have to. AND if the budget is super-tight, obviously dinner on the table is more important than a 250GB SSD... but for sure that's a sensible investment unless that $30-$35 is breaking point.

I still prefer the Ryzen build, but obviously the CPU is $70 more. So if that $70 is an issue with you, the i5 will certainly get the job done.
Some combination of those two builds is better. The GTX 1060 is much better than a 1050ti, but in the 1060 build you're paying $35 more for an older/slower CPU. And you can ditch the cooler unless you're really bothered by the stock Intel cooler.

Let me see if I can put something together for you...
 
So here's what I'd actually recommend if you can squeeze another $30 or so into the budget.
I've switched you over to a Ryzen 6 core which if you push a bit of overclock (you can do this with the stock cooler), should match or slightly outperform the i5 7400 even in gaming right now, while offering vastly better performance in any threaded workloads and **should** hold up much better in future.
Only 8GB RAM (but it's fast RAM), and a cheap SSD, but it's enough for now.

PCPartPicker part list / Price breakdown by merchant

CPU: AMD Ryzen 5 1600 3.2GHz 6-Core Processor ($299.00 @ Mwave Australia)
Motherboard: ASRock AB350M Pro4 Micro ATX AM4 Motherboard ($109.00 @ Shopping Express)
Memory: G.Skill Trident Z 8GB (2 x 4GB) DDR4-3200 Memory ($93.00 @ Umart)
Storage: Sandisk SSD PLUS 240GB 2.5" Solid State Drive ($109.00 @ Shopping Express)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($64.00 @ Shopping Express)
Video Card: GALAX GeForce GTX 1060 6GB 6GB OC Video Card ($345.00 @ PLE Computers)
Case: BitFenix Comrade ATX Mid Tower Case ($47.00 @ Umart)
Power Supply: Corsair CXM 550W 80+ Bronze Certified Semi-Modular ATX Power Supply ($95.00 @ Shopping Express)
Total: $1161.00
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-05-02 16:14 AEST+1000
 


i just changed some stuff on build 2 if you wanna check it out


 

That's probably about as cheap as you can go without making major compromises.

I've lived with a 120GB SSD and will never do so again, particularly when a faster drive with double the capacity can be had for ~$30 more.
You can manage a 120GB SSD if you have to. AND if the budget is super-tight, obviously dinner on the table is more important than a 250GB SSD... but for sure that's a sensible investment unless that $30-$35 is breaking point.

I still prefer the Ryzen build, but obviously the CPU is $70 more. So if that $70 is an issue with you, the i5 will certainly get the job done.
 
Solution
http://www.game-debate.com/cpu/index.php?pid=2463&pid2=2454&compare=AMD%20Ryzen%20R5%201600-vs-Intel%20Core%20i5-7400%203.0GHz

Even stock, the Ryzen is the better cpu for gaming, and by far for anything production, beating even an i7-7700k handily. 4c/4t is a minimum on many games, but many newer games, especially hard hitting or heavy server drop games, are already moving to take advantage of hyperthreading, so much so that the i7-3770K gets better, consistent fps than an i5-7600k, without the big frame drops on large maps or high server count areas.