The short hop answer is mostly correct, but
A
Arthur97
is also right.
The crux of it is the delay in the swing. Characters with faster short hops usually feel faster because they have less delay. For example, Fox
feels much faster than Wolf--even though they both have the same initial dash and air accel, and Wolf has more air speed. Part of this is because of Fox's dash attack, but it's mostly because Fox's short hop height is 24 compared to Wolf's 30. It makes a huge difference not just for pressure, but also for mixups--it's hard to react to what Fox does out of a jump because the Fox can just fast fall, land, and do nothing (with fastfall, Fox only commits 17 frames in the air if he short hops).
For Lucina and Roy, there's one additional insight needed to piece everything together--they're comparably fast, for the most part, but they're
using their mobility to do different things.
If you look at the raw numbers, you'll see that they're both very safe on shield--their frame data is full of -4s and -6s. But not all shield safety is created equal. Roy's shield safety happens when he's sweetspotting, hitting his blade. Lucina's shield safety applies at the tip. Meaning, if Lucina is up close, she can't swing if her opponent is in a position to shield, because she'll get punished for her swing. Roy, on the other hand, can swing even up close, or out of a spotdodge, or after rolling behind you. Just check out d-tilt--Roy's sweetspot d-tilt is -3 on shield. That's actually pretty insane, and Lucina has nothing comparable. Her f5 jab is -16 on shield.
What this means is that Roy is frequently using his mobility to
get closer to you, or just outright bursting toward you.
Meanwhile, Lucina is using her mobility to
fade back from you.
This makes it seem like Roy is much faster, because Lucina is frequently taking two steps forward and then one step back, while Roy is taking three forward.
The difference in short hop/full hop time is crucial to this. For evidence, watch how Leo plays Lucina and Marth. He'll dash away from you, dash toward you, then, right at the end of the initial dash forward, he'll jump and wait until he gets in position to swing. Here's one of these waits in action:
https://youtu.be/aElnFDOzxH4?t=52.
Depending on where you shield, he might even change how he uses the followup aerial. Here's an example vs. Larry's Wolf:
https://youtu.be/eAGtwdUUnUI?t=193 where Leo actually crosses Larry up based on where Larry was shielding.
Leo uses Marth/Lucina's additional hangtime in the air to make a snap-reaction based on how you've spaced. During that extra air time, he could be fading back, deciding to fast fall, or something else entirely, but the key is that Roy can't do this even with a double jump, since his air accel isn't high enough to get a sufficient fade back effect.
As a result, traditional sword zoning is much harder to do with Roy--but the tradeoff here is that Roy is really good against whiff punishers who usually beat traditional sword zoning.
For example, ZSS is really good at whiff punishing swords in this game--but of the swordsmen, Roy (not Chrom, not Lucina, not Marth) is one of her hardest matchups. Why is that? Because Roy runs up to her, shields or spotdodges or rolls, and then mashes jab and d-tilt and OOS options that she can't whiff punish. This is something that other swordsmen simply can't do.