The real difference
It isn't the features. It's what happens before you can use it.
Both track time by project and client, on your own server, with your data staying there. Where they part ways is the day you install them — and every day you maintain them.
Installing Kimai
You clone the repository with Git, run Composer to pull the dependencies, edit environment variables, run the installer from the console and set file permissions. Kimai's own documentation says “FTP installation is not supported, because most of Kimai's management tasks rely on the console”, and it needs a dedicated subdomain — a subfolder won't do.
Installing Hourexa
You upload a folder to your hosting by FTP or from your panel's file manager, open a page in your browser and answer three questions. The installer checks your server, creates the tables and your admin user. Subdomain or subfolder, whichever you prefer.
When something breaks
Kimai's support is the community forum — generous people, answering when they can. With Hourexa you bought a product, so there's someone whose job is to answer you, for the support period included with your licence.