I inherited an app that uses both Parse and Firebase. Parse is a much broader platform - a general-purpose database, server-side logic, push notifications, built-in support for common application requirements.
Firebase is a much more narrow product, focused on synchronized, realtime data management (think key-value store with pub-sub). e.g., my app uses Firebase for managing all the chats, but Parse for everything else.
If Firebase solves your backend problem, then definitely use that. It's simple, fast, cheap. But I think it'd be tough to create an analytics layer on top of it.
If you lack backend skills to manage your own servers, then Parse is a good option... but it's a proprietary system you have to learn and then deal with its limitations. When you can't make something work - especially database-related - you're just stuck... and you may find yourself writing a ton of backend code just to deal with those limitations... and then you run into potential cost issues if your app requires lots of queries.
"IoT" and "analytics" can mean anything... it's not clear whether you're applying realtime analytics to tons of streaming content or whether you're doing more data capture and periodic analytics - in that case you may want to dump the data into Amazon RDS or Aurora and then have access to any number of analytics tools that can run off of relational data.
Yeah, not terribly useful, but hard to recommend anything without understanding the application requirements.
The good news is that you can spend a couple hours with Firebase and a day with Parse and you'll know whether they can do what you want.