Conclusion and Price
So, Apple TV versus Mac Mini; which one should you get? Maybe price will help you decide. Apple TV retails for $229 directly from Apple. The cheapest Mac Mini retails for $599 directly from Apple. Thus, you could buy two Apple TVs for the price of one Mac Mini and still have $140 bucks in your pocket; or you could buy an Apple TV, an iPod Touch, and $170 worth of iTunes media for the price of a Mac Mini. But remember, an Apple TV is just a plastic case, hard drive, and wireless card. A Mac Mini is a plastic case, hard drive, dvd burner, processor, RAM, graphics card, wireless card, etc.
Still can't decide on the Apple TV versus Mac Mini? Consider what you will be using it for. It all depends on what capabilities you want in your home media setup. If you are strictly going to use your TV for watching shows, watching movies, and listening to music, it is strongly recommended that you go with the Apple TV and spend the extra money elsewhere.
If you want the ability to browse the Internet, use applications, play games, etc, it is strongly recommended that you go for the Mac Mini, as it will be worth the price.