I have an uncle who drove to the hospital when he had chest pains and lived. The ER doctor said he was having a heart attack and that if he had been there a few minutes later, he would have died before reaching the hospital. ER could not have gotten him there sooner -- even ER admitted that. He was within a mile of the hospital.
They may not have gotten him to the hospital quicker, but they are well equipped to treat any arrhythmias (abnormal heart beats) on the way to the hospital. He also would have arrived at the ER with IV access already established, oxygen on board, and an EKG already read and transmitted so the ED physician knew before he arrived that it was a heart attack, and what part of the heart was involved. If it took more than a few minutes to stabilize and transport him, the cath lab would be ready by the time he arrived for definitive care.
The paramedics do a lot more than just drive you to the hospital. An arrhythmia is what kills you early in the heart attack, and they are well equipped to deal with any arrhythmias during transport.
NEVER DRIVE YOURSELF WHEN YOU ARE HAVING CHEST PAIN