When driving in the US, at a 4 way stop intersection, the driver at the right has the right-of-way.

In England, does the driver on the left have the left-of-way? or the right-of-way?

I try to travel by hired car or train to avoid having to make such decisions....

I don't know where you have been driving in the US, but at a four-way stop, the right-of-way is determined by which car got there first, not just the car on the right. It then continues around with the order in which they reached the intersection.

That's how it works where I live too.

It gets more complicated when pedestrians are involved and, in SF, when streetcars are involved. In addition, if I am making a left turn, I am blocking the opposite lane which allows a car in the street in which I am turning to make a right turn out of sequence into the lane that I am blocking.

Rule in Michigan:
You reach a four-way stop intersection with a stop sign at each corner of the intersection. The driver who arrived at the intersection and stopped first has the right of way through the intersection. If two or more vehicles reached the intersection at the same time, the vehicle on the left should yield to the vehicle on its right. • You reach an intersection with a malfunctioning traffic signal. Come to a complete stop and yield to vehicles already at the intersection. Yield to the vehicle on your right if you both reach the intersection at the same time.

I can't ever recall a four-way stop in the UK. Not when I was living there, or now I am a visitor. Junctions are marked with priority normally, but in the unlikely chance you should come across one where it isn't clear then I would guess the one coming from the right has right of way, since they are likely to hit you otherwise! If you are turning and they are going straight on then they have right of way.
Pedestrians and cyclists going straight on have priority, not that you would notice it in my experience.

Have a look at the Highway Code. I haven't for quite a while I admit, and nor have most UK drivers since they passed their test!

Broken traffic lights in CO are treated the same as four way stops, which can be confusing if there are multiple lanes in each direction. For me, it's safety first, I'm not going to tangle with some aggressive driver who decides he has the right of way when he doesn't. I might curse at him under my breath, but not tangle with him.

We expats called the few four way stops we encountered in Kuwait as four way no stops. Those folks do what they want when they want. I was just happy to arrive alive.

The law in New York state says"

At intersections not controlled by signs or signals, or where two or more drivers stop at STOP signs at the same time and they are at right angles, the driver on the left must yield the right-of-way to the driver on the right.
Example:You are stopped at a stop sign and you are going to go straight through the intersection. A driver on the cross road has stopped at a stop sign on your right and is also going to go straight. You must yield the right-of-way to the other driver.

Same here, no sign or just a stop sign, not a four way stop, left yields to right.

The rule in Califronia is:

• Without STOP or YIELD signs: The vehicle that arrives to the intersection first has the right-of-way. However, if a vehicle, pedestrian, or bicyclist gets to the intersection at the same time as you, give the right-of-way to the vehicle, pedestrian, or bicyclist on your right. If you approach a stop sign and there is a stop sign on all four corners, stop first and proceed as above.

I live in CO. Unfortunately the driving here is nuts as many ignore even the basic rules. But then again, most of them are transplants from other states.

4-way stops ain't really a thing in the UK. Sure there could be some but I actually don't recall any. That is what Roundabouts are for. The car in the circle has the right of way (unless it is one controlled by traffic lights)

And junctions without a roundabout or lights have give way signs. As I said upthread I have never seen a fourway stop in the UK.
We have them in the Netherlands, with priority to the right. Just a rule everyone understands, but most junctions give an indication of priority through road signs and markings.

Fourways really only exist on tiny roads in the middle of the countryside where there is only ever one car. I can think of a few in such situations. But of course the real solution is in the mind of most Brits which is "after you" as queue thinking kicks in.

This thinking works well when traffic lights break down. Our town has two intersections which use this technology. The easy one has great visibility and is almost (but not perfectly) square. People slow down and manage the issue fine by signalling, catching each other's eye and waving, all very courteous. The trouble starts at the second one where two of the lanes are badly offset (medieval streets etc), and that can be difficult but again common sense kicks in.

In the US. the right-of-way doesn't determines the car on the right side.

Glad this got worked out, and for the seemingly universal agreement on the topic..

My rule: The car with the most unrepaired dents has the right of way. Or else.

But does that ever really happen, the EXACT same time? It always seems to me that one car really gets there first...... In that situation, I and most others let the other car go first, regardless. However, some people just can't help themselves. Honestly, I have never seen an accident in such a situation. What I have seen is over-politeness so that it takes too much time to sort this out.

I think the rule should be, whoever really needs to get somewhere in a hurry goes first.

Rules for the District of Columbia essentially always give pedestrians the right of way (known by at least some as the "right to die") and, at two-way intersections, the driver on the left is generally to yield to the driver on the right if they arrive at approximately the same time. The phrase "approximately the same time" is included in the municipal regulations.

After many years here and in other U.S. cities, I'm often amazed by how often cars arrive at two-way intersections at the same time -- or close enough for the difference to be moot. And while courtesy is sometimes seen, it is definitely not always on display.