There are mainly 2 types of voltage regulators with different types of power stages:
A) with a power-stage with low output impedance, like an emitter follower
B) with a power-stage with high impedance, like a transistor in emitter circuit. This output-stage is more current controlling.
Type A are the classical regulators like the 78xx series. Usually they have quite some drop from a Darlington output stage.
The low drop voltage regulators are thy type B), often with an PNP or P-MOSFET as an output element.
The different stages need a different compensation: the emitter follower version can get away with a simple single pol compensation. This makes it relatively easy and ideally it can get away with little capacitance at the output. For very tight regulation it may still use a more complicated compensation.
The low drop regulators essentially needs quite some capacitance at the output, often with a defined ESR. The compensation needs more than just a single pole.
How good the regulation is depends on the implementation. Especially the higher frequency performance depends a lot on the output capacitors and also the layout. There is a slight tendency for the conventional regulators to be better with voltage regulation, but worse with current regulation. However the need for the output cap can compensate some of this. NPN transistors tend to be a little fast, which helps a little for better regulation.