Which is a better set-up for gaming and youtubing out of the two builds below?

Problem with link 1:
Micro ATX boards don't offer a lot of room for upgrading. Your stuck with that motherboard budget or not once you get it- so be sure you are absolutely sure that motherboard is best for you. You won't be able to over clock or SLI/Crossfire support graphics cards together. Mini tower cases- that case may or may not be able to fit your graphics card inside… I'd recommend a mid-tower case. Reason being is when gaming, your computer is gonna get hot and mini-towers don't have a lot of room for air flow, so you could be making your components hotter in turn. I'd also change your power supply. Let your power supply have at least a minimum of "80+ bronze rating" for efficiency. The rating determines reliability. I bought a low end power supply not doing any research on them and it "blew up" in my computer 6 months later and killed my graphics card- so get a bronze rating at minimum- trust me, your saving yourself some problems.

Link number 2 issues: I'd get either an i5 or i7 over a Xeon. Xeon's are great processors- but they are meant to be inside server computers or computers that will be doing heavy stuff like rendering out 3D and CGI stuff for long periods of time. Would not recommend for gaming. Other than that- same issues as above with motherboard, case, and power supply. I'd also recommend getting two 4GB sticks of RAM and duel channeling them, makes things better.

You can still be within your budget by making those changes but perhaps going with an AMD FX processor or A10 processor. It's true Intel is better for gaming, but also more expensive. AMD is better for budget builds- I personally have used an FX 6200 and FX 8350 and was very happy with both despite it being "not as good as an Intel".