The i3-4150 is the better CPU all around. Heat, energy consumption, price/performance ratio, raw power, newer socket, etc.
And although hyperthreading doesn't help the i7s much (since they already have 4 amazing cores, games don't often use the extra threads), hyperthreading is a big positive for the i3s. Most people seem to forget i3s have this ability and just think of them as dual core i5s, but they're significantly stronger than that comparison would imply, as the potent combination of higher base clocks with HT is not something to ignore.
Since cost is a large concern, you may want to look at getting an R9 270 and overclocking it. R9 270Xs are just overclocked R9 270s. Other than the difference in clock speed (usually 900Mhz versus 1000Mhz), the card specs are identical.