When the DEF of “Thousand Needles” and the ATK of the attacking monster are the same, the attacking monster is not destroyed by “Thousand Needles”’ effect.
If the attacking monster is destroyed, it is destroyed by “Thousand Needles”’ effect, and it is sent to the Graveyard during the “send monsters to the Graveyard” portion of the Damage Step, at the same time a monster would normally be sent to the Graveyard because of damage calculation.