Google trends: swiftmailer is growing but phpmailer is still very strong.
I would go with Swiftmailer because documentation is clear and easy. Phpmailer site/docs are a bit messy (at least they look so).
EDIT: after trying them both (and banging my head against an hosting issue for which SwiftMailer did not output any type of hint) I completely changed my mind, I would definitely go with PHPMailer for at least one good reason: it's much easier to debug in the event you have any issue.
Both SwiftMailer and PHPMailer provide debug options (SwiftMailer with a plugin and PHPMailer by turning on SMTPDebug = 2), but SwiftMailer is made by hundreds of small files that make SwiftMailer more difficult to debug compared to the 3 files PHPMailer is made of.
And about docs, the PHPmailer documentation is less fancy looking, but it has got all you need: simple tutorial, examples