I like how easy it is to get up an running with push apps! It's not too difficult as some other platforms out there (such as Twilio).
There are no major downsides at this time of writing either - just make sure you know your target audience well if they're using multiple devices or operating systems because sometimes different OSs have differences when dealing with alerts/notifications etc which can be confusing. We use them in conjunction so we do send messages from our website through their platform but also integrate into native applications that run off mobile phones / tablets where users may access these via WiFi only networks such as hotels & cafes without data plans available.