It looks like Mandrill has already stopped accepting new accounts and are moving their service into the main MailChimp completely, so no-cost options are a bit more limited.
Both services are backed by decent companies. MailGun is run by Rackspace and SparkPost by Message Systems. I'm more familiar with MailGun, but they both look like good options for sending out messages.
Regarding pricing, MailGun is a more expensive service. If you're looking to maximize the number of messages you can send before paying, SparkPost will be a better option. One nice bit of MailGun is that it can act as an e-mail forwarder, accepting inbound messages and forwarding to a different address. SparkPost will only post incoming messages as a WebHook.