Historically, yes. There was a reason previously the CAA and EASA were historically happy accept the FAA's certification for new aircraft, on the assumption the FAA were very good at its job.
That no longer seems to be the case (given the fact that EASA now want to have their pilots fly the MAX before it returns to service), and there's well documented evidence (many news articles over the past few months talk about this) showing that over the past 10 years, the FAA's budget was drastically cut, forcing them to effectively outsource certification in part to Boeing to "self-certify".
That no longer seems to be the case (given the fact that EASA now want to have their pilots fly the MAX before it returns to service), and there's well documented evidence (many news articles over the past few months talk about this) showing that over the past 10 years, the FAA's budget was drastically cut, forcing them to effectively outsource certification in part to Boeing to "self-certify".