Western Union is the Bitcoin of USD, you send money to someone's number and they can pick it up in France or Nigeria with no accountability, and you can't get it back if you are scammed. For receiving it's better than receiving reversible bank/PayPal/(Dwolla) payments because of no chargebacks, but for sending, you could be sending your money to a Nigerian prince who will send you back nothing. It is like sending cash in an envelope, but with no clue who is receiving it.
Who should "go first" in such a scenario?
This would be good opportunity for a (trustworthy?) escrow service if you don't know the other party. The escrow service receives the Western Union cash and the Bitcoins, and only forwards them if both are paid. If the service is trustworthy enough for you to send Bitcoins to it, they might as well simplify the service - just buy your Bitcoins and send the WU themselves though (like an exchange with WU withdraw does).