I was going to say that PHPMailer is no longer developed, and Swift Mailer is. But when I googled …
https://github.com/PHPMailer/PHPMailer
That suggests its being worked on again.
I’ve used PHPMailer a lot, and its always been solid and reliable. I had recently started using Swift Mailer, for the above reason, and it too has given me no trouble.
Now that PHPMailer is developed again, I think I’ll probably give the new version a try.
So, my answer is that both are capable, and that it doesn’t matter that much – choose one, learn it, use it. Both offer massive advantages over mail() and abstract away the nuances of email so that you can get on with whatever you are really trying to develop.