The LM338 is not a switching regulator. It's a linear one. Each one is 5 amp capable, and the parallel operation scheme you've shown provides 20 Amp capacity. But, lets say you feed it 40V DC, and it is set for a 14.5 V dc output. The V differential is 25.5 V (dropped across the four components) at 20 Amps is 510 watts dissipated into the 4 - LM338's heat sync.
I've used this part before in electronic circuits. It's good at regulating. But, not very efficient. Unless you keep the input to output voltage differential small, it's going to make heat and waste power. Thats' why it is offered in both a TO-220 package for light duty applications and a TO-3 Steel case unit for toasty ones.
I'm not saying won't work. But, the shunt types will be less parts, less complexity, and possibly little or no heat advantage.
As for reliability/longevity. The reliability of a unit goes down with the increased parts count. Each component has a failure rate. For example, say a resistor has a failure rate of 100 hours. If you have 10 resistors your unit failure rating is 1 in 10 hours. More components give a higher probability of unit failure. I couldn't find a reliability rate spec for the LM338, quickly. But, active components are usually lower numbers than passives, and higher operating temps lower their rating even further. For an overall reliability rating, you select the lowest rated part, and reduce that number every time you add another part by a factorial of the added part's rating. I can tell you it is NOT easy making high reliability products for mil spec installations, or critical communication installations.
Cheers,
