Hi Corey. Thanks for your interest in our products.
The Events Calendar (TEC) is the free/core plugin to run events. It doesn’t have any integration or conflicts with http://wp-events-plugin.com/ that I’m aware of, but it’s typically not advisable to run 2 calendar plugins on the same site.
…Or you might be interested in running Events Manager (not our plugin) along with Event Tickets (ET), our free/core plugin to handle RSVPs, which has a paid add-on called Event Tickets Plus (ET+). I haven’t tested if ET and ET+ work seamlessly with the Events Manager plugin, but it is designed to be able to work for our events calendar plugin and others’.
Last but not least, we have a pretty great Refund Policy so you can buy one or many of our add-ons and thoroughly test them.
Let me know if you have any follow-up questions.