It's not a matter of choosing which policy. Most (but not all) insurance companies have an agreement that in cases like this where there is what's called dual indemnity (cover by two policies) that it is the driver's policy that deals with the claim. Where insurance companies are not in the agreement then it is shared 50 50. Crucially however in either case it is only the driver's bonus that is taken.
The driving other cars element is Third Party only but if your friend has comp on their policy then they can claim under that separately although there may be bonus implications here and if damage is minor might not be economic.
From your point of view just report it to your own insurance company and they will deal from there, no need for your friend to worry about their bonus.