Speaking from recent experience, i had my 24-70mm front element scratched, the coating wore off due to it rubbing against my jacket and the center of the element was scratched from something else.
The removal of the coating doesn't make any noticeable difference to the images i took however the scratch did. I spoke to the cannon service center and they said that under both circumstances the cheapest and quickest option was for them to simply replace the element. That was still at a cost of $700 AUD though.
The best advice here is if the front coating is damaged but not scratched, check you photos and see if you can honestly notice any difference.
Failing that, take it into your service center and ask their opinion on the matter :)