I don't honestly think Oda emphasizes the 'underdog' angle in most fights. Zoro was as infamous in the East Blue as any of the enemy Pirate Captains they faced. Luffy always felt evenly matched with his adversaries. I guess you could say he was an 'underdog' against Crocodile, one of the Seven Warlords. He had a type advantage fighting Eneru. Lucci was really powerful and defeated Luffy the first time they fought. Once Luffy revealed the gears, he and Lucci were very evenly matched.
Oda tends to draw tension from the situation rather than a perceived difference in fighting class.
More often, the narrative focus seems to be on Luffy being underestimated by his enemies. In a classic 'underdog' story like Rocky, the protagonist is underestimated by their opponent, yes. But importantly, the audience also recognizes that Rocky Balboa, an almost washed up boxer from South Philly, is punching above his weight in taking on the heavy weight champion of the world, Apollo Creed. There have been situations, like when Luffy first fought Crocodile, where the elevated status of the enemy is used to set reader expectation that Luffy is outclassed.
More often, enemies underestimate Luffy to their own peril. In these cases, the reader feels like they're in on a secret that the enemy isn't. When Luffy throws down with a powerful opponent who looks down on Luffy, the more common reader response is to say "ooh boy, they're in for a surprise!" rather than "Wow, this enemy way outclasses Luffy! I have no idea how he can take on an opponent of this caliber!"
Once Luffy took down a 'Warlord' class opponent in Crocodile, however, that 'underdog' status is sort of dissipated in the battles against Moria and Doflamingo. Sure, they are powerful opponents. Maybe more powerful than Crocodile. Maybe more powerful than Luffy. But Luffy isn't really an 'underdog' in the classic sense.
Luffy was in way above his head during the entire Paramount War saga - and that was sort of the point. Luffy lost his crew. He lost his brother. It wasn't a story where the plucky underdog achieves victory against all odds. Survival was a miracle. Luffy may not have achieved victory in any major battles, but he did win the favor of many important allies, which allowed him to live to fight another day. The hand of fate guided Luffy, an ant, through the hurricane of the paramount war. He failed to achieve his goal of saving Ace, but he proved his moral character to a number of important allies who will likely ultimately help to change the world some day.
Doflamingo was more powerful than Luffy pre-Gear 4, but I don't really think Oda drew much tension from the fact that Luffy was an 'underdog'. The reader wasn't really wondering 'how can Luffy possibly fight a Warlord of the Sea?' Oda didn't really draw any tension in the conflict from 'disparity in class' between the protagonist and the opponent. So, sure, maybe Doflamingo was more powerful, but I never considered Luffy an 'underdog' in the Dressrosa arc.
Luffy does feel like an underdog against Kaido and Big Mom. I think the fact that so many readers don't think Luffy is ready to cross that threshold yet is testament to the fact that Luffy is an 'underdog' in the battle against the two Emperors. The reader response when Luffy says he's going to whoop two Emperors and Linlin responds derisively, the reader doesn't think 'just you wait until you see what I know Luffy is capable of.' Instead, the reader is more inclined to agree with Big Mom in thinking Luffy is too early to pit himself against such a powerful enemy.
I don't really think that the series as a whole can be defined as a series of conflicts in which Luffy has been perpetually framed as an underdog. There have been specific instances where Oda derived tension from that particular dynamic; in Alabasta, during the Paramount War, and again in facing Linlin and Kaido.
Personally, I don't think Oda is ready for Luffy to take down an Emperor solo yet. There are narrative reasons to think Luffy won't be alone in the battle against Kaido. We'll probably see a few flashes of the monstrously strong person Luffy will soon become in this fight, but ultimately it will be a team effort. It allows people to think, 'wow, Luffy's almost there!', while also still showing that he's a few steps below Roger and Whitebeard in their prime.
So to summarize, there's a difference between Luffy fighting someone who is seemingly more powerful and Luffy being an underdog. The 'underdog' dynamic is a narrative tool for creating tension which Oda has used on occasion, but isn't really pervasive in the series as a whole. There are frequent instances of opponents underestimating Luffy, but as his star has risen, there are just as many instances of his reputation preceding him.
Croc or Enel would never.
