Would somebody care to sell me on why this is superior to SendGrid or Amazon Simple Email Service? (Or perhaps what use cases it better serves.)
Detailed searchable mail logs: we actually tell you what happens to every single one of your messages - nobody else is that brave!
Incoming email push - and our parsing/cleanup of incoming traffic is pretty impressive - if it's time to self-promote, it's now. And our incoming email handling if flexible: we do routing/forwarding, similar to Rails/Django routes.
Storing/hosting your email traffic and giving POP3/IMAP access to it - nothing stops you from giving each user of your app their own email address. Some customers do that very, very creatively.
Piping it through some battle-tested Mixpanel-powered analytics doesn't hurt too: some companies charge an arm and a leg just for that one feature.
Mailgun is not about merely pushing mail, we're more of an "sexy programmable ESP" :) We're just a bunch of oddballs who thought that running an ESP business would be fun!
I personally have a hard time parsing how much money $0.5 is. I'm assuming you're charging 50 cents per 1K messages. My mind groks $0.50 per 1K messages, much more easily.
to some degree, customers make up their own minds about what's "better" when comparing two products/services that may be identical in functionality and pricing.
Someone may prefer the colors/logos on one site vs another, some may prefer where one is located (located in my city/state/country vs the competitor). Some may care about the technology, wanting to support one supplier vs another.