When we're talking regulated vs resistor, we're talking about 12v pixels and how they step down the 12v into 5v which is required by the LED's (each pixel has 3 LED's in it, red, green, & blue).
A regulated pixel uses a regulator to step the voltage down, so if we look at both sides of a regulated pixel we'll see the WS2811 chip on one side and the regulator on the other. Both sides will have a black square chip on it. The regulator takes in a voltage and drops it to 5v, so if we feed it 14v it will drop it to 5v. Similarly, if we feed it 8v it will drop it to 5v. It's a sharp drop from a higher voltage to 5v. There's a point; however, where the input voltage is too low for the regulator to work and every pixel after that will be dark.
A resistor pixel uses a set of resistors to step the voltage down, so if we look at both sides of a resistor pixel we'll see the WS2811 chip on one side and some resistors on the other. The resistors take in a voltage and drop it down a set percentage. If we feed a resistor pixel 12v it will drop it to 5v, but if we feed it 8v it may drop it to 3.5v.
Where the difference becomes important is as we move down the string, further away from our power source, we lose voltage due to resistance in the wire. The regulated pixels will all look uniform until a set point where they no longer function. This is the point in the string where the input voltage has dropped too low for the regulator to work. The resistor pixels will gradually lose the intensity of their brightness as we progress down the string, eventually reaching a point where the difference in brightness becomes noticeable and white starts becoming pink. They won't have a set point where they drop out. Instead they will slowly fade to dark as you progress down the string.
So Which Do I Choose?
In reality, you're unlikely to notice much of a difference unless you are maxing out the ports on your controller and at that point you'd likely be power injecting anyways. When you power inject, the difference becomes moot because you're bumping the voltage back up around 12 throughout the line.
All of that said, when I first started, I thought regulated were the way to go, so I paid the premium for them. Over the years, I have transitioned to resistors for any new additions to my personal show.