Postgres version upgrades are basically painless, at my workplace our upgrades complete in so little time our users don't notice, and we have more data than probably 99.9999% of companies out there (mature company in aerospace industry).
Version upgrades for SQLite are basically a no-op though, that's kinda one of the reasons why it's so great to run in production (and deployment a maintenance being mostly a no-op as well, apart from setting up backups I guess).
I don't actually suggest that everyone should run their production on SQLite, but it's genuinely worth considering especially for small-ish projects.
The difference is only in the deployment/maintenance.
And considering the context he stated, zero downtime really doesn't seem like something he's worrying about.
I personally find Postgres WAY easier than SQLite simply because of the deployment story. I do a lot of hotfixes and dangerous stuff on personal projects, and having two databases complicates that tremendously. I like being able to run hot code on prod.
For the record, this is not the same reason I like postgres for actual production code