Who pays for the damages in this Asiana-Aeroflot collision?
Short answer:
Someone's insurance company is writing a check.

Longer answer:
What usually happens in the insurance world is both insurance companies write checks to repair their respective clients' aircraft.  The insurance companies may then fight it out between themselves to determine who is responsible for what, if it makes financial sense to do so.

In cases where injuries or deaths result from an incident it almost always makes sense for the insurance companies to fight it out(those payouts can run in the millions of dollars).

In cases like this where there's only equipment damage the cost of the repair will determine how aggressively Aeroflot's insurance carrier pursues getting their money back from Asiana's carrier.  If we're talking about extensive and expensive structural repairs into the millions of dollars Aeroflot's insurance carrier will be motivated to get someone else to pay the bill. Conversely if the insurance company can make their money back through Aeroflot's premiums and pursuing Asiana for negligence or something along those lines to try to get them to pay for the repair would ultimately cost more (money and time pursuing the case) than just absorbing the loss the insurance carrier will just absorb the loss.