That's a good question. The answer is HomePod will integrate with the apps you already interact with daily on your iPhone. Shortcuts is bringing the abilities of apps in the world's largest App Store to HomePod. Siri observes your routine as you use your iPhone, creating shortcuts that you can access from anywhere in the Apple ecosystem, no extra systems needed. Alexa is an external, separate system that you have to maintain in addition to the one Siri does for you on your iPhone.
Second, HomePod will centralize the control of your home into one system — HomeKit — that you can command from your iPhone, your Watch, your Mac, your AppleTV or simply through voice as you walk around your home with HomePod.
Lastly, and most importantly, no Amazon speaker comes close to sounding as good as HomePod. It's a pretty incredible little speaker. If you enjoy music, you owe it to yourself to listen to it on excellent speakers. It really is an entirely different immersive experience.
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So, I've gone and found answers to my original question since nobody here has answered it. The answer is different today than it would have been 6 months ago. Amazon Alexa has 30,000+ Skills. HomePod couldn't match that. It was an advantage for Team Alexa, something that Alexa could do that HomePod couldn't.
But that's changed. Every day, new apps are updated with Siri Shortcuts support. There are 2 million apps on the App Store. iOS 12 with Shortcuts has only been about for 4 months and there are already hundreds of supported apps. As the first 1.5% of those apps update with Shortcuts support, Siri will have caught up to Alexa's 30,000 Skills. What makes this inevitable is that developers don't even have to intentionally make a Shortcut like devs need to program Alexa Skills. They just need to flick a switch in Xcode to enable Siri to automatically suggest Shortcuts for their app to their users.
What automations won't HomePod match that your Echo can do? I'm not being facetious; I'm genuinely curious.