The "game features with the same name" rule from the DMG errata says:
Different game features can affect a target at the same time. But when two or more game features have the same name, only the effects of one of them—the most potent one—apply while the durations of the effects overlap. For example, if a target is ignited by a fire elemental’s Fire Form trait, the ongoing fire damage doesn’t increase if the burning target is subjected to that trait again. Game features include spells, class features, feats, racial traits, monster abilities, and magic items. See the related rule in the “Combining Magical Effects” section of chapter 10 in the Player’s Handbook.
The use of "for example", indicates that damage is one game feature effect – but there are others that are left unspecified. Similarly, in the corresponding PHB entry, the use of "such as" indicates that bonuses to hit and to saves are also game effects, but others are possible.
Unfortunately, we are not given much guidance in terms of what constitutes a more potent effect, other than by referencing the Fire Form trait (and the Bless spell in the PHB) it is clear that ‘points’ themselves (actual resultant points of damage or bonuses to saves or to hit) are not a measure of potency, but their base dice are.
When considering two overlapping spells of the same name, one that has been altered by a sorcerer’s Metamagic feature and one that has not, which Metamagic features result in a spell of greater potency?
I am posting my current thoughts on this as an answer below, but am interested in seeing contrasting arguments and reasoning. Also, a better answer than mine would include official Metamagic options available beyond the PHB.