Would it be a good choice to use a Mac mini as wireless router? I know that I can use network sharing to share my cable network connected to Mac mini and turn it into a Wi-Fi hotspot.

I haven't purchased a Mac mini yet. From the description on Apple Store, Mac mini currently has a 802.11ac wireless connection.

I believe using a Mac mini won't perform as well as a Airport Extreme, but I have very few wireless devices(an iPhone, a Macbook and a Playstation), so would there be any big difference between using a Mac mini and an Airport Extreme?
I'd say it's not a good choice. Apart form the energy usage there might be some compatibility issues (since it's an ad-hoc network) and you are quite a few options short (no port-forwarding for example). If budget is an issue, get a cheap router, it will likely still perform better than using the Mac as a router.