Which PC is better for gaming?

By the specs the HP is the way to go and i'm not too sure about full graphical settings etc. But both those games should definitely run if the settings are tweaked.

Nope and nope. Not enough horsepower or memory, from either. Minecraft *maybe*, bit no chance of running GTA.

Both are not good enough to play minecraft (needs 2 GB of RAM minimum), but should be able to play GTA San Andreas. The first one doesn't state what Pentium 4 so I can't really say which one is better.

Buying an expensive item is not a good idea unless you can get it from a Local dealer. Somebody with a door you can Knock down when it goes bad.
No Hard drive means you have to buy and install your own.
Preferably you want a machine that has:
- Intel CPU Core i7 3770 3,4 GHz,
- Nvidia GPU GeForce GTX 770
OR
- AMD CPU AMD FX-8350 4 GHz
- AMD GPU Radeon R9 290
with
- RAM 8GB
- OS 64-bit Windows 7 or 64-bit Windows 8 (8.1)
- DirectX 11
- HDD Space 40 GB

At the least:
- Wndows 7/Vista/XP PC (32 or 64 bit)
- Quad-core Intel or AMD CPU processor
- 4GB System RAM
- 6GB free HDD (Hard disk drive) space
- DirectX 9.0c compatible NVIDIA or AMD ATI video card with 1GB of RAM: Nvidia GeForce GTX 260 or higher; ATI Radeon HD 4890 or higher
- DirectX compatible sound card

Neither of those PCs are worth spending any money on. And because one of them doesn't have an HDD that's like $50 (plus another $100 if you don't have a copy of Windows or something) right there.

The Athlon 64 X2 is better than a Pentium 4 most likely but it's not worth buying because it's an old processor with no real upgrade potential. Your money is better spent on a newer system. You can put together a budget gaming PC for about $400 that wipes the floor with both of those.

Neither are very good, but the HP one is slightly better. I'd suggest getting a new PC, but if you want to keep/optimise your HP machine, here's all the upgrades you can do (note that I don't know what games you want to play, but if you do all of these, your PC will probably play most smaller "indie" games, as well as meet the minimum requirements for some large "AAA" games like Rome 2 Total War and Civ V BE):

1. I don't know what your OS is, but upgrade it to 7 premium if you don't have it already.

2. I'm not sure what motherboard you have, so you may be stuck with your Athlon X2, but look up your socket and see if you can upgrade (the X2 in your CPU means it has two cores, so get the one with the highest number after X). If no CPU's for your socket have more than two cores, you probably shouldn't bother upgrading and save the money for either something else on this list or a new computer.

3. Upgrade the RAM. Again, I don't know what Motherboard you have, but look it up and find out what type of RAM it supports (Probably DDR2) and how much. I'd suggest 4-8GB. Try to get your RAM in sets and at the same speeds/by the same manufacturer (for example if you get one 8GB stick you're fine, but if you get 2 4GB sticks, try to have them both the same).

4. Upgrade Your Hard Drive. I'm not sure how much you were planning, but I'd suggest at least 512GB.

5. I'm not shure what kind of GPU you have (although I assume it's some kind of integrated one). If you don't want to spend any extra money, go into your BIOS and increase the *amount of RAM being allocated to it (the way you do it varies depending on your motherboard, so you may want to find a tutorial on Youtube or something). If you are willing to give up some cash, get an ATI HD 2000-series Graphics card, or an Nvidia 9000 series. Anything more will probably be bottlenecked by your CPU and be a waste of money.

*Note that increasing the amount of RAM your GPU can use may take it away from your CPU. I wouldn't suggest doing it until you upgrade your RAM, but if want to, you can test different configurations to see if any of them run games better.

I know this is a long answer, but here's what I suggest when getting a new PC:
Windows 7 Premium
Intel four-core CPU or AMD six-core CPU
Dirextx 11-compatible video card with at least 1GB of VRAM
8-16GB RAM
1TB Hard Drive