Ebbie: the two sides of the head are not symetrical because this is also true of the rest of the body.
The body's cavities would need a complete re-design to encompas a heart which was central, and which had its major vein and artery (assuming still only one of each) entering/exiting centrally.
The intestines could not be fitted in as well unless there were two identical intestines (one turning left and folding, the other turning right and folding).
Duplication of internal organs such as intestines, veins, arteries etc., would lead to a possible back-up of material inside the body. Say e.g. one intestine provides a little more pressure, the waste material if not expressed would be forced back up the other intestine.
Blood flow would be complicated, and blood pressure would need to be equal in both complementary systems to avoid a flow reversal on one side.

Just some idle meanderings!

Nigel