It kind of depends. EMTs are able to do some things, paramedics are able to do more things, and the hospital itself can do even more things.

I live about 6 minutes from the closest ER. If an ambulance can get to me in, say, 3 minutes, it's still not clear if it's better for me to get myself to the ER on my own. Maybe I get an ambulance with EMTs who aren't trained/authorized to do what needs to be done for me. Maybe I really need to be at the hospital within 8 minutes or I'm going to die, and waiting for an ambulance just isn't going to cut it.

But I think, statistically, people should usually prefer to wait for the ambulance. It's just that specific circumstances can make that the wrong move, but most people won't know when that's the case.