In reply to Bottom Clinger:
I have both BirdNET and Merlin.
Merlin does the id in real time. I suspect that means that it is processing on your phone. That means that it doesn't need a data connection, and it doesn't need to store or read any files from your phone, if you are worried about that sort of thing (although, obviously, it does need access to your mic).
BirdNET sends the data off to a server at Cornell for processing. That means that it needs to save a file on your phone, and it needs a data connection (although you can send audio off later).
Both apps are owned and run by Cornell University, and both are biased towards N American birds. Both seem ok with relatively common birds over here (although I have had some obvious mis-identifications). I don't know how well they perform with rarer birds.
I have found BirdNET to be a little more sensitive, but Merlin has a nicer interface and is easier to use.