Is Diddy Kong outclassed compared to other monkeys?

Like in the last game, Diddy can use his Barrel Jet to hover temporarily. The problem is that this seems rather pedestrian compared to Dixie, who can actually gain height and so outranges him both vertically and horizontally. Even underwater, Diddy's linear jet boost seems harder to use effectively than Dixie's consistent speed increase. And while his Kong Pow turns enemies into Red Balloons, after the first world I found myself having more then 90 lives all the time (the max being 99), and Dixie's Golden Hearts are much better for actually staying alive in the first place.

Does Diddy have any redeeming qualities whatsoever? Or is he just straight outclassed?

I think your analysis is about right. I believe that Dixie is superior to Diddy Kong in almost every way.

As you said in your question, Dixie's extended jump and golden heart abilities are better than Diddy Kong's abilities, and unlike Cranky Kong's spike-proof high jump, there aren't any situations where Diddy Kong's jump is useful where Dixie Kong's jump wouldn't be at least as good. Since the jump and high-five abilities are the primary things that change between companions, Dixie beats Diddy.

In multiplayer, it looks like Diddy has one advantage over Dixie: He can use his gun on the ground. See this wiki for a more detailed comparison.

Watching some of the fastest records in the speedrun mode, it appears that in some situations, Diddy is the most useful companion when swimming. It seems that Dixie's hair twirl lets you move through water quickly, but Diddy's rockets give you so much more control over your direction that, for some specific strategies, he's more useful, or at least faster.

I recommend watching world record replays on water levels to see how and when Diddy and Dixie are used by top players.