I had this problem intermittently. Sometimes iPhone and ipad reminders synced and sometimes not. I got chat and phone support. Apple support was patient and tried everything I had already tried. Nothing worked. I finally just manually entered my desired list of reminders into icloud.com then deleted the icloud account from both the phone and pad. I re-entered my PW to add the acct and after a few seconds everything repopulated. It has synced between devices fine ever since.
The steps would be:
Be sure everything you sync to the cloud from all devices is there (on PC go to icloud.com) You may have to manually complete your reminder lists on your PC if they never made it to the cloud. My notes and calendar all synced fine all along so I just had to double check that my reminders were in the cloud.
Go to utilities>settings>icloud>delete account. Confirm at the new window that you want to delete all items from each device. (Scary but it's still on the cloud). Your account email address should still be showing at the account info section. Just enter your Apple PW and wait a few seconds and it will all repopulate.
I think my issues started with iOS .6 Apple support seems unaware many folks are having issues but 2 support folks and a supervisor tried very hard to help me. The intermittent nature of the sync issue made it hard to know if their solutions were working. This "account delete" seems to be the answer for me at least. Good luck.