And to generalize that -- when the load resistance is already above the generator resistance, it's better to stay on the high side, i.e. reduce the load by merely maintaining load current. When below, it's better to stay on the low side, i.e. increase the load by maintaining load voltage.
(We might measure the load in terms of average load resistance: instantaneous V / I. Note this is different from the AC incremental resistance of the load, and is simply the ratio of numbers measured with a meter, no fancy differencing needed. Note also a "heavy" load is a low resistance, because we always speak of load in terms of conductance, but resistance is reciprocal, go figure.)
A linear regulator passes the same load current, while dropping the excess voltage; average input resistance is thus proportional to peak voltage, and so rises during the surge.
A TVS passes the same load voltage, while drawing excess current; average input resistance is thus inversely proportional to peak current, and so falls during the surge.
Note that a switching converter does even better than these possibilities, because as voltage goes up, current drops roughly proportionally; it has a constant-power characteristic and doesn't care what the input voltage is, as long as it's within operating range.
A switcher will still have some resistive characteristic remaining, for example switching loss tends to be significantly higher at high voltages. This can be designed to be a fraction of total load power, making it still much easier to handle than the power absorbed by a brute force (series or shunt) method.
Load dump generator resistance is generally tested at 2 ohms or thereabouts (depends on the alternator ratings in the target vehicle), so the decision point is at a fairly low resistance, and lighter loads like this will graciously choose the first option.
I suppose very low loads, like audio power amps, might opt for a shunt method; with a customized switching controller, they might even try and turn on both switches simultaneously, shorting out the supply and clearing the fuse. A more subtle case would be partially turning on the switches, using them as a power shunt regulator instead. Though, transistors aren't good for absorbing much energy, so this probably wouldn't work well until you get into the really big (multiple kW?) sizes, which can pretty much absorb the full pulse anyway without special effort.
Which, the peak available power is in the kW -- so, anything in that middle range of impedance, and not big enough to just grin and bear it, can save a huge amount of trouble just by shutting off completely. Which can still be done through a series or shunt method -- in series, the switch opens, drops all the peak voltage, and load current drops to zero; in parallel, the switch closes (crowbars), sinks all the peak current, and load voltage drops to ~zero (which eventually turns to the series case, as a fuse must open -- there will still be a 12V baseline after the surge, and we can't have that crowbar staying on forever!).
Tim