We use Mailgun at work, and I can attest to its consistency and performance in inbound mail processing. Our webhook is consistently hit within about 1 second when I send a test email to our app's email.

I will say that Mailgun's UI could use a little bit of help. There are a number of things that make it feel half baked, but in terms of functionality, as aforementioned, it's not lacking.

We were, hitherto, considering the possibility of using Mandrill for outbound mail, only because they seemed to offer more spam folder avoidance knowledge and analytical data, while Mailgun was (and is) surely preferable for inbound... that switch will never happen now.