Both are going to need a hard drive. One only has 120 gb, and the other only has 60.
The first build is a solid build with current parts, but with that small case, you won't be able to get much more put into it. You will have to get a larger case if you ever want to upgrade. The 750 ti is a nice little card that packs a good punch in current titles. The only problem I see with this build is the size. I personally hate small porta-builds. They are hard to keep cool if you tax them, and they are usually hard to upgrade due to lack of space.
The second build needs a PSU, but it's also a first gen i7. They're great processors that people loved to overclock hard. That being said, how much more life would that thing still have if it's been overclocked since release. The plus side to this build, (not sure how bad pricing is) but you could easily get a new motherboard and processor and use everything else, along with the new power supply.
If it were me, I'd go with the second build, run it for what it's worth and eventually buy an fx-#### processor and motherboard. Everything in this build would carry over, including the noctua cooler (most likely).
Either way, you're looking at buying a secondary drive for space anyway. I don't see anyone making it very long on a 60 gb or 120 gb hard drive with current titles taking up 30 gb of space along with windows taking upwards of that.