The question is a bit off-topic for SO (IMO) and is (kind of) asking for opinions but it may be worth a high-level answer. I use both platforms daily.
Core Data and Firebase are two unrelated platforms used to (manage and) store data; it's hard to directly compare them without understanding your use case.
CD is a framework used to model objects in your app. It's the 'front end' of data storage, where the 'back end' could be SQL, flat files, plists etc. It's more of a single user concept which stores data locally on the device (it has cloud functionality but that's a different topic).
Firebase on the other hand is a live, event driven, cloud based, multi user capable NoSQL storage. While it offers off-line persistence, that's really for situations where you need to be interacting with data when the device is temporarily disconnected from the internet.
It is not correct that:
firebase documentation about it not being able to filter and sort at
the same time
But, your Firebase structure is dependent on what you want to get out of it - if it's structured correctly, it can be filtered and sorted at the same time in a variety of very powerful (and faaast) ways.
Core Data is really an incredible technology and building relationships between objects is very straight forward and has SQL-like queries for retrieving data.
If you are looking for a database that leverages local storage - go with Core Data or another database that's really strong locally such as Realm, MySql and a number of others.
If you want to have Cloud based, multi-user, event driven storage, Firebase is a very strong contender (Realm is another option as well)
I would suggest building a very simple To-Do type app and use Firebase for storage in one and then build another using Core data. Should only be a couple of hours of work but it will really give you some great basic experience with both - you can make a more informed decision from there.