I own both and I think it depends on how you want to use it.

Both require power and wireless home network.

Chromecast needs a PC, tablet, or phone to cast netflix, hulu you tube, etc....It does not work well with apple based products. You can cast from apple products but apple does not support casting from the most common apps such as playing movies or music that were purchased from itunes. You would need to convert these files into another format to cast them. if you do not use itunes or apple products, you would be happy with Chromecast.

Apple TV is best when you also use apple products but does have advantages even if you do not have an apple account. The apple device can play netflix, showtime, hbo go, and about 30 other channels without the need of having another PC, phone or tablet connected to cast which is better from chromecast in that you need to use another device to cast hbo go etc. The way it works is that you go through and authorize your apple tv for each channel which is a time consuming onetime process. For example, you pay for hbo through verizon fios. From apple TV, you can log into your verizon account and authorize the device to play HBO. It is the same process for each channel...showtime, fox tv. For non TV items such as HULU or Netflix, you log in through apple tv. Once you go through this setup, all you need is the apple tv device to play it to the TV through your TV and your wireless connection. for apple users, you can also access all of the music and movies on your icloud, ipad, iphone, or itunes library on your PC.