It's not hard to make your computer, but if your mother says you're not allowed, you're not allowed.
If you're asking which the better build is, its the second one because of the stronger GPU, but that doesn't mean the rest of the build is trash.
Your CPU is alright and GPU too, if you're planning on playing Minecraft and League of Legends. (my old 5570 could run both)
But beware, your Power supply on both builds are not very reliable, and it could die taking your whole system with it.
To save some money you can cut out the DVD reader, and the CPU fan. (use the stock one and don't OC.)
Also, get rid of that trash Power Supply.
This would save around $58.
Given you want to keep the same budget, (I'm using the $500 one) I would get rid of that PSU and replace it with a little more expensive but reliable Corsair CX430, and then with whatever may be left, try to upgrade your graphics card.
PCPartPicker part list /
Price breakdown by merchant /
Benchmarks
Power Supply: Corsair Builder 430W 80+ Bronze Certified ATX Power Supply ($39.99 @ Newegg)
Total: $39.99
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2014-03-09 13:45 EDT-0400)
That PSU takes up $40, leaving you with $18 to add to your GPU budget.
Your GPU right now is $70 so we can add that to $18 and remove it.
Your new budget is about $90. Here's the best I could find:
This is a good card and will run most if not all your games you're trying to play at 1080p, but if you're going after BF4 and such, stick to low resolution.
PCPartPicker part list /
Price breakdown by merchant /
Benchmarks
Video Card: Sapphire Radeon HD 7770 GHz Edition 1GB Video Card ($89.98 @ OutletPC)
Total: $89.98
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2014-03-09 13:48 EDT-0400)
Hope I helped.