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For one, Heroku has dedicated customer support when you pay them.

Right, dedicated support should be available at launch. Thanks for the feedback.

That difference is very clear: you still need to buy and manage your own (cloud) server to run dokku on.

Having used both extensively, the answer is as simple as one is private/hosted and the other is open/self-hosting.

Heroku is easy, but expensive. Dokku is more work/management, but cost-effective.