One can certainly understand the differences that may be required to handle heavies, or even just jets, given their mass and the spool up time etc however it seems there is no clear picture even for SEP GA.
That's probably because "SEP GA" covers a very broad range of types that can be flown at a broad range of speeds.
1) Operating at or close to the bottom of the drag curve, it's not possible to make sustained corrections reliably with pitch. Whether you pull or push, your glideslope gets steeper. As you move away from the bottom of the drag curve, the trade off between speed between glideslope changes gearing. A substantial change in glideslope adjusted by pitch causes only a small speed variation.
2) At the same time, as speed increases, the phugoid period increases in proportion. When you add thrust at a constant AOA, the primary effect of the thrust increase is a speed increase -- equilibrium isn't instant, and it takes some time for that speed increase to get turned into a change in glideslope at the original speed. The time required for it to "sort itself out" is proportional to the phugoid period.
3) Faster aircraft tend to be powered by more complex powerplants. While the turbine with a substantial spool time is an extreme, turbocharging and even constant speed units cause short delays between throttle movement and response. That makes it harder to make fine adjustments with power.
All of those make this game horses-for-courses.
The technique that works best at visual approach speeds in a C152 and the technique that works best for a turbo-charged Bonanza flying an ILS approach may well be different.
FWIW, the best mnemonic I even learned for the ILS was DFWTP: Don't ...er... Fiddle With The Power.