I have no personal experience, but have researched it a bit because I would like to fly again.
I met someone that had their Permobil C500 destroyed by an airline (I believe it was United). The airline replaced it with a new Permobil F5. It took some time for that to happen, and this person was in a loaner chair (from the airline) until the F5 was delivered. I think her trip was long over by then. It was an interesting way for her to get a new wheelchair!
Another thing to consider is that not all wheelchairs will fit into all airplanes. For most power wheelchairs, the back must be removed for the wheelchair to fit into the cargo hold of smaller aircraft (such as a Boeing 737). My Permobil C500 Corpus 3G has an easily removed back. My Permobil C500s VS does not have a back that can be readily removed (I think the shop rate is about 2 hours for that job). That wheelchair could only fit in the cargo holds of large aircraft (Boeing 777, for example).
So, you need to figure out what kind of airplane you will be flying and determine if your wheelchair needs to have parts removed to fit in the cargo hold.
The research I have done indicates that damage can occur, but that there are steps you can take to reduce the likelihood of the wheelchair being damaged. Even with those steps, I would only consider flying with my backup wheelchair.
Here are steps I have read about or have been told by others who fly.
1. Remove the joystick, seat cushions, and anything that can become detached from the wheelchair (headrests, leg supports, thoracic supports, backpack, etc). All of that should go with you in the cabin as carry-on luggage or be checked separately.
2. Put the wheelchair in its most compact position. Most likely, remove the seat back or fold the seat back down onto the seat
3. Wrap the upper part of the wheelchair in plastic (like is used to secure items on a pallet).
4. Disconnect the batteries. On my Permobils, that is easily done by moving a switch which throws the circuit breaker.
5. Put the wheelchair in freewheel mode.
6. Take pictures
You want to make it hard to impossible for the airline baggage folks to set things in your seat. You want evidence that there was no damage to your wheelchair before you turn it over to the airline. If the plastic wrapping is damaged where the wheelchair is damaged, it is easier to make a claim against the airline for that damage.
I have talked to quite a few folks that have travelled with their wheelchairs and read many stories of others who have travelled. I would not hesitate to travel in the US with my backup wheelchair. I hope to do so this year.
Steve