I haven't done either, but think about how you want to see the Canyon:
Helicopter would be a broader area, but all from above (flights below the rim were banned ages ago after too many crashes...).
Mule would be below the rim, but probably not much further than a hike. My only experience with mules was on a Boy Scout hike in Havasupai Canyon (an offshoot of the Grand Canyon), when one of the kids in the troop burned his foot while camping, so a mule had to be rented to get him to the top of the rim (~12 miles or so from the campsite). Even without a burned foot, it didn't look like fun...
But read the other Grand Canyon thread -- I highly recommend driving along the rim to the East entrance. Nice views of the canyon along the way... Then grab lunch at the Cameron Trading Post.