Two months ago I wrote this:
It's very unlikely that the version of WordPress you use affects your email delivery.
So turns out I was very, very wrong. WordPress 4.3 includes a newer PHPMailer with additional security options, and this seems to be causing problems for every PHPMailer-based plugin. This is one of the reasons Postman still works when others don't.
One of the PHPMailer plugins quietly disabled part of SSL to get around the problem. Always be careful of the code you install! If you're not reading the source code at least read the reviews :-/
See https://wordpress.org/support/topic/easy-wp-smtp-setup?replies=3#post-7613727