I have a head unit that supports both. I used CarPlay for a year, and then I switched to a Moto X Pure, so I use Android Auto now.
Note: I'm going to state a bunch of negative stuff up front, but there are good reasons why I continue to use this platform, so stick around 'till the end.
One of the primary motivating factors in me switching to Android was CarPlay's instability with my iPhone 6. It would crash every single day, sometimes multiple times a day. Often, when I connected the phone, I could try playing songs but there would be no sound, the only solution for which was to disconnect and reconnect the phone. Android Auto does not have these issues and has been much more stable.
Otherwise, they're both similar, and they have similar limitations. Browsing music on either platform is pointless. It's not something you're intended to do; hell, Android Auto will actually lock your screen if you try to scroll down more than three or four times in list views.
Both platforms support voice search using Siri and Google Now respectively, but you can't actually do anything useful in terms of finding music to play. You can try to ask Siri to play a song by name, but it might not interpret your request correctly, or it will play a song by that name that is a different song than what you intended. In the case of Google Now, asking it to play a particular song will always pull from Google Play Music regardless of what your preferred music app is or what music you have on your phone.
So, for music and podcasts, your best bet is to create a playlist before you connect your phone and then browse to that playlist from your app of choice. Some podcast apps, like Pocket Casts, will maintain such a playlist for you automatically, making them much simpler to use.
Why, then, use either of these? Well, as it turns out, voice search is really great for responding to messages. On CarPlay, you can dictate messages (via the Messages app) to Siri, who will read them back to you and confirm that you want to send them. Works really well. Android Auto works similarly, with two major differences:
1) you can do this for any kind of message that you receive, including stuff like WhatsApp; and
2) With CarPlay, you respond to messages by browsing to the Messages app on your home screen, finding the message, having Siri read it back to you, and then responding "Yes" when asked if you want to reply. With Android Auto, you hit the Voice Search button and say "Reply" to respond to whatever was the last message you received. That's more convenient, but it's also the only way to respond to messages; there's no way to browse for a specific message.
Navigation via voice search is similarly useful. It's great to be able to just get into the car and say, "Hey Siri, take me home". Both platforms work really well here.
Using voice to conduct operations on the phone is the killer app. I'm disappointed that such functionality is limited to built-in apps only. You can't say something like, "OK Google, play the Rock Moods playlist on Spotify in shuffle mode". In the nearly two years that I've been using these platforms, I've seen no indication that this is ever going to change, despite all the voice search innovation that's happening outside of the automotive electronics industry. That's a big disappointment, but I'd still argue that these platforms are worthwhile if you do a lot of messaging.