There doesn't appear to be an option in Reminders to 'move to another list'
Is it really just a case of copy and paste, which would be pretty terrible
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Using iOS 6.1.2 it is pretty straight forward (I have no older version of iOS with me to check how and if it works there, but I guess it will).
Tab on the task/reminder you would like to move to another list. Choose more options or show more (my language setting is German so I'm not 100% sure how this menu item is called in english). There appears an option titled List. This will allow you to move the item to another list.
My iPad is currently at IOS 9.1. I was able to move an item from one list to another by
Clicking edit (upper right corner)
Selecting the red symbol to the left of the item
Choosing the "More" option (in gray)
Clicking "list" (fourth option down from the top)
Choosing the list to which you would like to change your item.
Hope this helps!