Installing a 3 wire in place of a single wire is not that uncommon, especially if using headers.
Not sure about a 4 wire. Most don't go through the extra trouble for it.
The one wire has no heater and single signal wire back to the ecm. Ground though the body of the sensor.
On a three wire there's a 12v that hooks up to acc for the heater, a ground wire for the heater and a signal wire. The ground for the signal is done through the sensor body.
On a 4 wire, there's heater power and ground, signal wire and the forth is a dedicated ground back to the ecm.
To use a 4 wire in a system originally a 1 wire you would have to run a wire back to the ecm and see if it uses s dedicated pin for o2 sensor or ground the 4th wire somewhere out in the engine bay to mimic the stock ground path.
Signal should be the same. All narrow band sensors range from .2-.8 volts IIRC and use the same rare element voltage production method.
A 1, 2, 3 or 4 wire is no more or less accurate than the other. OEM's are all narrow band sensors that works around stoich but not much else. The most tangible benefit of a sensor incorporating a heater is sooner into closed loop operation or the ability to mount it further away from the exhaust port.
In the case of sooner into closed loop in a stock location, you're talking a few minutes at best. A stock location is selected by the OEM engineers in consideration of getting the exhaust gas to get the O2 sensor up to temp quickly (316 C) and keeping it above that temp.
When relocating further away from the exhaust port (ie: aftermarket headers), the difference is (or can be) significant. Sometimes its the only way to keep the sensor hot enough to function due to thermal losses over the extra length of pipe and the reduced thickness of tube headers over cast manifolds.
