So I've got two choices here. If i go with the Haf 912, i can get an aftermarket cooler (Cooler master hyper 212 evo). But if i go with the design define mini i can't, but it is a much better case. Also being a budget build, My CPU is a Athlon x4 760k (Is that necessary? Its just $10 more than the 750k), Mother Board is a micro atx which is compatible with the Haf 912, and a R9 270x. If i do go with the Haf, it leaves me room to upgrade to a standard atx mobo later, and a aftermarket cooler. But the Fractal is just better. So if you we're me, what would you go with?
For a budget build go with the 750k, it will be fine. As for the case, the HAF 912 has the support for the ATX mobos and generally good airflow.
Admittedly the mini has the better looks. However it should be fine, you can get good enough micro ATX mobos anyway if you want to upgrade at some point.
So both are good choices. I would still probably side with the HAF912. And offer another choice with the Antec 302.