The transformer-based unit is a (two, for stereo) multi-tapped auto-transformer. It's main advantage is what's called impedance-matching, meaning it presents a constant impedance to the load side, for use in multiple-speaker installations.
They often also have several load-side taps for selecting relative distribution of power, beneficial when using dissimilar speakers on a given channel, and/or in areas of different volumess. The instructions are usually clear on settings.
The variable resistor-based units, sometimes known as L-pads or T-pads. A simple variable-tap unit changes the line-side impedance; adding one (L) or two more (T) has a bit less power loss and better line-side impedance control.
The transformer-based units have a reputation for better fidelity, as well as quietness and the above-mentioned impedance selections. They are power-limited, but, if the power levels are that high, you should be using separate amps.