SQL Scotsman explains synchronous versus asynchronous stats updates:
With that said, it would seem that asynchronous statistics are better suited to OLTP environments and synchronous statistics are better suited to OLAP environments. As synchronous statistics are the default though, people are reluctant to change this setting without good reason to. I’ve worked exclusively in OLTP environments over the last few years and have never seen asynchronous statistics rolled out as the default. I have personally been bitten by synchronous statistic updates on large tables causing query timeouts which I resolved by switching to asynchronous statistic updates.
This is an interesting, nuanced take on the issue. My bias is toward asynchronous stats updates because I have been burned, but it’s interesting to read someone thinking through the implications of this seemingly simple choice.