Even in the US, response times can really vary. As an extreme example, in Jersey City (population ~300k) there were a bunch of incidents a couple years ago where residents called 911 in an emergency and no one answered.
E911 (location information sharing) also doesn't work consistently.
The advantages of coming in an ambulance are traffic priority, priority attention in the ER, and medical triaging and coordination. The disadvantages in the US can be extremely expensive to some people if they don't have the correct insurance and inconsistent timeliness.
The advantage of coming in a private vehicle are speed (usually), but at the disadvantage of having to get past ER gatekeepers and lack of information and preparedness. It is probably wise if possible to have a third person in the vehicle call the ER at the destination hospital to let them know what generally should be expected.
Another issue is that it's inherently risky to live more than 30 minutes driving distance from a major city hospital. To do so basically necessitates a life flight which is extremely expensive and not necessarily quick either.
The for-profit, gotcha capitalism monopolization of hospitals and medical services by private equity also results in worse, deadlier patient outcomes, hospital closures, and more expenses. Medicare for all (m4a) isn't a fix because of the Medicare Advantage scam, the medigap scam, the part D scam, and the lack of long-term care, skilled nursing, dental, vision/glasses, mental healthcare, and hearing aid coverage that doesn't provide true comprehensive single-payer healthcare at a sane cost per patient and with better outcomes.
If you live in the PNW/Hawaii and more than 30 minutes, or you go skiing, hiking, mountain biking, boating, or commute on highways that could take excess ambulance time think about getting a Life Flight membership. Know someone who is active outdoors but don't know what to get the for XMas, might make a good gift?