page speed insights is run in a datacenter somewhere and will definitely have different performance characteristics than running Lighthouse on your local machine.
github.com/GoogleChrome/lighthouse/issues/6708#issuecomment-466170107
Pagespeed's test machines are more than likely slower than your local desktop, and are causing scores to be lower than if you run them on your machine.
github.com/GoogleChrome/lighthouse/issues/6708#issuecomment-466563685
Pagspeed didn't use lighthouse before v5 and wasn't actually performing analysis of your site, but more checking it against a bunch of static rules (eg: compress your scripts, use small images) and it added up to a final score. That's why it was more consistent.
github.com/GoogleChrome/lighthouse/issues/6708#issuecomment-468977091