So yeah, it’s canon that hobbits are the stealthiest of the races of Middle-Earth, even more so than elves. Which is an amusing trivia fact, until you start realizing how much of the plot of both The Hobbit and Lord of the Rings is based on this.
Why did Gandalf randomly decide that a plump gentle-hobbit was the right person to be a burglar for an adventuring party? It seems like wizardly eccentricity, until you realize Bilbo’s got a racial bonus to Stealth of like +20. Why does he get the Ring? In text, it’s partly coincidence, but also - which party member do you give your Ring of Invisibility to? The Rogue with a crazy Stealth bonus, of course. Bilbo uses his Stealth, boosted by the Ring, constantly, and the dwarves would have been dead a dozen times over without it. He’s able to get the Ring in the first place because he stealthed out of the middle of a horde of goblins. Then he’s sneaking up inches from trolls, secretly living inside the elves’ freakin palace (with Legolas) for months, rescuing a whole pack of dwarves from under the elves’ noses, regularly pick-pocketing people including elves, sneaking past a dragon, sneaking to deliver the Arkenstone.
Then we follow up into Lord of the Rings. Gandalf’s now bred up a second-generation Rogue. Frodo, Sam, Pippin, and Merry have that same massive racial Stealth bonus, and Frodo also has been raised by an adventurer. He speaks Elvish fluently, he’s friends with dwarves, he studies maps obsessively. Then he inherits Bilbo’s Stealth-boosting magic item - now upgraded to cursed McGuffin. When Gandalf decides it’s time, he collects Frodo and assembles a party. Their goal isn’t to march into Mordor, or to battle the Boss: it’s to sneak through enemy lines, past an entire army (or two).
The humans, elf, dwarf, and wizard angel keep drawing too much attention and getting them attacked (plus admittedly Pippin, the low-WIS darling), so eventually Frodo and Sam ditch them and head off on a pure stealth run. They can’t use the Ring of Invisibility anymore, but fortunately Galadriel gave them another Stealth-boosting magic item, the cloaks. They sneak halfway across Middle-Earth, past armies, through miles and miles of enemy territory, while being hunted by every evil being on the planet, particularly a literal giant All-Seeing Eye. Not to mention the Palantiri, extremely powerful divination items which are being actively used by three different groups of enemies/competitors.
The other main canonical Hobbit power is that they’re “very hardy folk”, meaning they have incredibly high resistance to various things from poison to mental influence. So they can survive the literally poisonous air and water of Mordor, which was designed to kill every species but orcs. And they can survive close contact with the Ring for decades or centuries, not only physically but also maintaining some degree of mental independence, when any other race would succumb in minutes to hours. (Note the most “powerful” characters - Elrond, Galadriel, the literal angel Gandalf - refuse to even touch the Ring, as do the most morally sound, Aragorn and Faramir.)
Why did Gandalf choose a minor member of the country gentry, the size of a toddler, with no combat training, to save Middle-Earth? Because absolutely no other creature on the planet could have done the task. Frodo was all but created as a weapon against Sauron. He, and he alone (with Sam), was capable of saving Middle-Earth.
TL;DR: Legolas would get jump-scared by Frodo every single time, because Frodo is the greatest Rogue in Middle-Earth, and the plot of the entire series depends on that fact.