And I also don't really follow what it would mean to assess dramatic mode from the perspective of Gygaxian mode, or vice versa? As far as I understand, the modes are approaches to playing RPGs - so I'm not really sure what it means to treat them as frameworks of assessment.
I am in a similar boat. I don't know what is meant by "assess" here.
So, let's look at Tomb of Horrors, played with D&D as the ruleset, but by two groups - one in Gygaxian mode, and one in dramatic mode. We must accept that D&D doesn't have a lot of tools for the players to work dramatic play, but the players are trying it anyway.
Step 1 - Why are we even going into this death-trap?
Gygaxian mode: Well, there's treasure and traps, and something powerful at the end to kill. Let's go!
Dramatic mode: No, really, why are we going in there? (Note: The original module actually doesn't give an reason to enter the tomb.) GM, you going to give us something? Is a rival also trying to enter the tomb to get a powerful item with which they'll threaten someone we care about? Has Acererak become some sort of threat? What is the narrative frame for going here?
Step 2 - Engaging with the elements of the Tomb
Gygaxian mode: lots of puzzle solving ensues.
Dramatic mode... in the first 15 areas of the original Tomb, there is one, and only one, creature that might talk - A gargoyle. It has low intelligence, doesn't speak common, and by gargoyle stats is 90% likely to just attack the party. The gargoyle has no stated desires or motivations. There's no new information about Acererak, or any other motivator revealed. So, other than basic physical danger, there's no source of dramatic tension or plot in there. The Players are working with whatever they brought in with them....
Folks here have seen the Brendan Frasier/Rachel Weis The Mummy, from 1999? Maybe that's what Tomb of Horrors looks like - the characters work through inter-personal relationships with the stresses of danger as a sort of driving inspiration. Gygaxian players may wonder why there's, oh, a budding romance developing while figuring out if someone's getting disintegrated by a Sphere of Annihilation, but hey....