Hi Joy,
Thanks for checking out our plugins!
If you have both events plugins activated on your site at the same time, you will likely encounter some issues like conflicts with slugs (which you can change in our plugin by going to Events > Settings > General). It would be best to avoid having them both activated together if possible. Either way, your first step before starting the switch will be to back up everything, just in case something goes wrong!
I would recommend first exporting your events from Event Organiser, deactivating it, and then installing and activating The Events Calendar. At this point, you will be able to import your events.
It looks like Event Organiser lets you export to CSV using the free Event Organiser CSV plugin. You can import a CSV to both The Events Calendar and Events Calendar Pro, so that may be your best way to go about switching over. For detailed information on importing with CSVs, please take a look at:
Importing Data from a CSV File
CSV File Examples for Importing
I would also recommend using a staging site to test this out before implementing it on your live site. A plugin like WP Staging will let you quickly and easily create a copy of your live site, which you can then use for testing.
If you need any help with this, please let me know!