These are technologies that operate at different layers. You can assemble an architecture using a combination of these.
AFNetworking is a good drop-in replacement for NSURL + NSURLRequest + NSURLSessionTask + NSURLSession. It's a client-side networking framework. It's a good choice if you write your own web server.
Most BaaS platforms have web APIs. AFN would work well with those. So would NSURL*.
Some BaaS platforms like Firebase offer an iOS SDK. In that case you could use the SDK instead of AFN or NSURL*.