Is there any advantage to catching Shield Knight?

Catching Shield Knight in the final catch scene will slightly change the dialogue.

If you fail to catch Shield Knight before the final boss, she will say "...you came for me." instead of "...you caught me."

If you are speedrunning the game, catching Shield Knight will end the scene early. If you don't need the money from killing enemies, you can even die to make Shield Knight fall earlier.

Outside of speedrunning, there is no advantage to catching Shield Knight.

Sources:

• GameFAQs: What happens if you don't catch Shield Knight? (Spoiler)
• Random Games: Shovel Knight - What if you don't catch Shield Knight?
• Gellot: Shovel Knight: Final Boss - The Enchantress [No Damage/Magic]
• Speedrun.com: Shovel Knight Any% Drake's Route

If you're trying to speedrun the game, it's slightly faster. The dream sequence ends as soon as you make contact with Shield Knight, so trying to catch her will end the sequence sooner.

However, what has a greater effect here is that Shield Knight will begin falling immediately if you get killed by the enemies during the dream sequence. The current Any% world record does a combination of the two, dying and getting knocked into Shield Knight's path, to end each dream sequence as quickly as possible: