You lose nothing if every export is on your own drive before you cancel. Circle has three exports, and each comes out as CSV. The member export comes from the admin and holds names, emails, profile fields, tags and which spaces each person can see. The community data export is requested from Circle support and holds your spaces, posts, comments and events. The Payments export holds subscription and transaction history.
The community data export does not include images or files uploaded to posts and comments. Save the ones worth keeping by hand, starting with your most read posts, and upload them again on the new site. Courses are not part of these exports, so copy lesson content across as you rebuild each course in Learnomy.
Keep the subscription and transaction files even though they cannot be imported as live billing. They tell you who was paying, on which plan, so you can invite each paying member to the right plan on your site. Circle documents each export in its help centre: community data, members and subscriptions and transactions.