Local only.

Even if you pay for their subscription, when you get to a new computer you need to manually authenticate with each service. But, it remembers which accounts you have, so it's faster than manually setting up each account from scratch. Basically "we know you have Gmail, xmail, ymail - tap each account to reauthenticate"

It's a good way to have (part of) the convenience of a cloud service, while combining it with the security of local only clients.

Edit: all of this is optional, you can choose not to let their cloud service know of any of your accounts.