I feel the exact same way; Sunshine's controls are part of the reason its my favourite Mario game. They're just so much more fluid and conducive to advanced maneuvers than the controls of the later games.

Sunshine's controls are just faster than Galaxy's controls in a lot of ways. In Sunshine you can start gain momentum on a dime. I like the side flip in particular; for one, it carries momentum perfectly (as you stated), but it can also can be initiated from a standstill, allowing it to double as a backflip. It's overall really versatile; probably the most useful incarnation of the move in the series.

The reason that I love Sunshine's movement the most, however, is because of how well the individual moves link into one another. It allows for an incredible level of movement.

A small, but cool example of the optimizations possible can be found in this speedrun. In this clip, Mario begins spraying a pianta with the regular nozzle. He then cancels the spray into a backflip by holding back and pressing A. Backflipping in Sunshine causes Mario to spray a ton of water forwards, cleaning the Pianta, but it sends Mario backwards and has a pretty large cooldown. The runner then instantly negates the backwards momentum and cooldown of the backflip by cancelling it into a dive with B, pushing him forwards very quickly. With this trick, Mario can clean off the Pianta almost instantly, while retaining forward momentum and wasting very little time.

This is just one small example of the movement in Sunshine. In reality, almost every move in the game links together extremely cleanly. In addition, most moves can be linked into a dive, which can then be cancelled into a ground-pound. This instantly negates all momentum from the dive, making precision platforming much easier for the casual player (like myself) than in other games. FLUDD is another great tool to aid precision platforming, and also affords the player great aerial flexibility, as well as being cancelling nicely into a dive for a quick return to the ground.

So even though Mario is faster and less heavy than Galaxy Mario, I would argue that Sunshine gives you even more tools and safeguards for precision platforming.

And it isn't hard to do either! While it might not be easy to link moves as cleanly as the runner in the video, making use of the amazing movement options in Sunshine is very doable for a casual player. I used a small example above, but there are countless ways where the movement just flows much better than Galaxy. And this is coming from someone who played Galaxy first! Sunshine's controls are just far more fun to me.