Which build is better?

I see you are very limited on funds at the moment, but trust me when I say you don't want to start out this way. I did, and it cost me several hundred dollars more slowly upgrading in the long run.

First your hard drive and power supply are fine, but you can get a bit more if you just wait and get a computer later. Here is what I would recommend for your cheap Intel based build for the motherboard, RAM, and case.
http://www.newegg.com/Product/Product.aspx?Item=N82E16811154095
http://www.newegg.com/Product/Product.aspx?Item=N82E16820313080
http://www.newegg.com/Product/Product.aspx?Item=N82E16813138394

The motherboard here has better power control, more connections for add on cards, better audio, and its pretty much the same price.
The computer case I changed only because it needed to be bigger to fit the bigger motherboard.
The RAM you will end up paying over $80 if you buy one stick at a time, and you risk issues with compatibility or that RAM type going out of sale. You are much better off to buy your RAM all together.

For the CPU, getting an i3 is a great idea for a budget system, but if you spend $50+ on a CPU to use until you can afford it you will end up pretty much tossing out that $50+ as you won't get hardly anything out of it to sell back. The point here is if you buy slow like that you will spend more in the long run and have a worse computer system. The graphics card you can do that with and add-on cards or disk drives, but you are best to get the main parts all at once.

As for the i3 graphics, they aren't bad. Compared to your laptop it will probably feel like you are playing games way better already as the graphics are probably better even without a graphics card. So it wouldn't be so hard to wait on a graphics card.

For an AMD based system:
http://www.newegg.com/Product/Product.aspx?Item=N82E16813130753
http://www.newegg.com/Product/Product.aspx?Item=N82E16819113359

For the AMD based system the hard drive, power supply, PC case are all fine. The RAM I think you should use the same RAM I suggested in the Intel build. For the motherboard, this one seems to be a bit better, has more hard drive connectors and a little better specs but if money is really tight the first one you listed will be fine also. The CPU again you want to get one and stay with it, but if you get the CPU I suggested you can avoid buying a graphics card entirely. That means for around $350 you could buy and build your entire computer and not need to upgrade it anymore. So that is an advantage.

Thanks for the support runedj4

So yes like both of us are saying its just better to gather more cash first. I didn't think about operating systems, if you want windows that will run you an extra $90 at least. Though Linux will do a decent job while you save up for Windows.