Pretty sure Gaia wouldn't be using a barometric altimeter, which would explain the difference.
Glad to hear it worked it for you. Travis was telling me all the guides are using it these days too - "Gaia Guide" or something like that they are jokingly calling it.
I find it is always low on elevation gain. Today it told me my gain was 810m when the net difference between my start and highest elevation was 960m. My watch said th elevation gain was 1000m.
One thing to consider with battery use is that I find that my phone will not turn off when the app is open so make sure to turn the screen off after checking it. I find that this is the most common reason why I run the battery down quickly.