4-pin fans are PWM fans, so they can be controlled by a motherboard's 4-pin socket. 3-pin fans have positive, negative, and sensor wires so you can hook them up to a motherboard socket or a fan controller (or directly to the power supply with a molex adapter).
The ones that are controlled by heat (IE: 4-pin fans hooked to a motherboard's CPU header) are controlled by the board itself, speeding up or slowing down the fan going by the board's temperature sensor(s).
Whichever is "better" depends on your usage. If you want a fan controlled by the motherboard for a 4-pin header, you'd want a PWM fan. If you want something with more power (38-mm thick San Ace, Panoflo, or Delta), you'd need a fan controller as the board's headers won't output enough power. For most standard 120mm x 25mm fans you'd just get whichever one you need between PWM and non-PWM/standard for your board headers. So just use whichever you want really.