In the original film Han shot Greedo without Greedo pulling the trigger at all and it made Han a bith ruthless, very much like Indiana Jones in the raiders of the lost ark, in the fixed up version Han shoots second. (Greedo is a terrible shot, cant even hit a target that sits still on point blank range)
guess this says it all http://www.starwars.com/community/askjc/rick/askjc20020905.html