When Google processes a page, it treats hreflang tags in the sitemap and in the page’s HTML the same.

This comes from a short exchange Google’s John Mueller had on Twitter:

He also clarified, later in the exchange, that putting hreflang in a sitemap vs. in the page HTML doesn’t affect when Google processes the annotation, assuming Google’s seen the sitemap before.

So, it’s much easier for the website owner to manage their hreflang tags through the sitemap, but for SEO purposes it won’t have a direct impact. Since hreflang implementation can help make or break your international SEO, website owners should stick with the method that works best for them.