Birding has 7 letters and 2 syllables.
Birdwatching has 12 letters and 3 syllables.
None of the other distinctions that people have suggested have really stuck.
In my experience, “birding” has taken over as the dominant term among people who talk about it a lot, probably because it is easier to say and shorter to type. This may be the origin of the idea that “birders” are more competitive or numbers-oriented: people who are like that are more likely to be talking about it a lot!