One issue with the authenticator apps (eg. Google authenticator) is that if you reset your phone, you lose all your secrets and need to reset 2FA for all your accounts. With the Yubico authenticator, the secret is stored in the key and the phone only gives a time signal and authenticates to the key over NFC. The app is also available for desktops, making it pretty easy to use 2FA without having your phone.
The NEO is older unfortunately, so it's only available in USB A form factor and has weaker crypto than newer Yubikeys (2048 bit vs 4096, iirc) for private keys stored in it if you're planning to use GPG (for email encryption or signing git commits). In practice, that's not a real limitation.
However, it also does not support signing Docker images, which is unfortunate.
If you're thinking of getting the USB C versions of Yubikeys and using them with your phone, it does work but since the Yubikey appears as a keyboard, it disables the Android keyboard while it's plugged in. If I remember correctly, U2F support on Android also requires installing the Google authenticator app even though you might not store any codes in it.
You'd think it would be easier to have these things working.
Edit
Perhaps not as it seems it doesn't work with 2FA in Chrome. https://forum.yubico.com/viewtopic31fc.html?f=35&t=2798