The easiest way to move files between accounts is through a shared folder.
You can now move the files from the shared folder to other places in your Dropbox. Once the files are moved out of the shared folder, they are no longer accessible from the Dropbox of your other account. You can choose to leave the shared folder or keep it around just in case you ever need to exchange files between the accounts again.
If you already have shared folders in one account and want to access them from your other account, be careful! Moving them into the new shared folder will cause you to leave the shared versions of these folders. Your local copies of the folders will no longer sync with changes other members make. To avoid this, keep the shared folders where they are and invite your other account to join the folders (or ask the owners of the folders to send invitations).