Don't remember where I found this or who told me this, but this is what I had in my notes:
A user session is counted before the page fully loads. While Google Analytics requires the full page to load. This can cause a discrepancy between the two systems. When a user visits an event online, they are assigned a unique ID that stays with them the rest of the service. We count how many unique ID’s are assigned and call that User Sessions.
Google Analytics is a way more complex and battle tested service than our dashboards and a lot of churches have different ways of calculating attendance. My advice would be to pick a system that works for you and consistently use that system to track growth.
So for us, we track both. Google analytics records/tracks itself, and CHOP summaries once a week I'll plug into Church metrics to keep an idea on it. I don't have the time (or desire at this point) to hone in on Google analytics and try and pull JUST the results for when service was actually going, as opposed to someone who came to the page when there wasn't a service or a search engine crawling.
We use both and recognize that both have their limits, but worry more about trends over time compared to the same data source a month and a year ago to see how we're doing in that sense.