So you're considering the Harman Kardon Invoke over an Amazon Echo. Or, more specifically, the $150 Echo Plus, which is closer in price to the $199 Invoke.
Both are smart speakers. Both have "Skills," which let them hook into services like music or connected home products or, well, whatever. Anything and everything.
Echo's Skills hook into "Alexa," the personification of Amazon's digital assistant. Invoke's Skills run through Cortana. Eventually these will all be one and the same. Amazon and Microsoft have a reciprocal deal that will let Cortana use Alexa, and Alexa use Cortana. We're not there yet, but it's coming.
How badly do you want to make Skype calls through a speaker?
No matter, though, because there's really not much that the Invoke (again, via Cortana) can do that the Echo can't. In fact, there's only one that that stands out.
Amazon Echo can't make Skype calls. The Invoke can.
That's a big deal, I suppose, if there's somebody you want to talk to over Skype, and if you only want to do it over the Invoke and not through a phone or computer. I'm not convinced that's a reason to buy the Invoke over an Echo, or Google Home. Sure, you can also dial up a phone number via Skype. But Amazon and Google do that, too. And both of those do a lot more (for a lot less money) than the Invoke.
OK, the one other thing Invoke does that the Amazon Echo doesn't is Cortana and Bing. That's inherent ot the platform, though.
At the end of the day, though, that's a pretty short list for those asking us this question. And neither of them is a particularly good reason to pay more money for something that ultimately does, for the time being, much less.