On some level Mixpanel is a competitor. You can send it events and query/extract them later. Mixpanel is geared towards app/web analytics and marketing-type purposes. Mixpanel gives you some tools for building queries and reports and lets you export to Excel. Keen is geared towards developers. You can build charts that you can embed in other webpages (which is very cool) but building the queries kinda needs API access.

If you're creating a custom analytics tool that integrates tightly with your system, Keen might be a better choice. Especially if you're going to e.g. let your customers view and analyze their own data (but not see anyone else's), Keen is a no brainer. It's got a better API and much better API security model.

If you're looking for something more akin to a Google Analytics replacement but event-based instead of pageview-based, Mixpanel or similar might be better.

Keen and Mixpanel both had great support, by the way. I'd encourage you to reach out to one or both if you're curious about how to integrate with it.