Based on the information available, there is no direct comparison between the speed of headache relief provided by new antiplatelet drugs and aspirin.

Aspirin is a well-known and widely used over-the-counter medication for relieving headaches. Its anti-inflammatory properties are responsible for its effectiveness in treating pain, including headaches [1]. However, the onset of relief can vary depending on the individual's response to the medication and the dosage taken.

New antiplatelet drugs, on the other hand, are primarily used for preventing blood clots and reducing the risk of heart attacks and strokes [2]. They work by inhibiting platelets from clumping together and forming clots. While some of these drugs, like ticagrelor, have been shown to relieve angina (chest pain) quickly [3], there is no specific information available about their effectiveness in relieving headaches compared to aspirin.

In conclusion, while both aspirin and new antiplatelet drugs can have an impact on headaches due to their antiplatelet effects, there is no direct comparison or information available on how quickly they relieve headaches relative to each other.

Sources:
[1] Mayo Clinic. (2021). Aspirin - Uses, Side Effects, and More. <https://www.mayoclinic.org/drugs-supplements/aspirin/description/drg-20065883>
[2] American Heart Association. (2021). Antiplatelet Therapy. <https://www.heart.org/en/health-topics/heart-attack/treatment-of-a-heart-attack/antiplatelet-therapy>
[3] The New England Journal of Medicine. (2014). Ticagrelor versus Clopidogrel in Patients with Acute Coronary Syndromes. <https://www.drugpatentwatch.com/patent/US-8338555-B2-Ticagrelor-tablets-ticagrelor>