There are characters in the media who are known, simply put, for being less-than-dangerous. They might even be The Load, or at least a Damsel in Distress. When danger rears its head, the character generally beats feet and lets their tough-guy friends deal with the problem.
But then, for some unexplainable reason, when the work is being adapted into another type of media, the character is made a bona fide Badass. The reasons for this are myriad. Regardless of the whys, there are two things to consider with such a change:
On the other hand, the character may have been The Scrappy whose job was to get captured by the bad guys and give a Damsel in Distress for the hero to rescue. Making them competent in a fight and no longer The Load can also result in a more preferred version of the character. In fact there are many examples of such a change becoming a Ret Canon to the original character.
Mowgli is an international spy who can fight wolves with his bare hands and win. In this case, though, his awesomeness compared to the original may be mostly due to the fact that we're seeing a grown-up version.
Amy has always been a fairly realistic character for her age. You don't expect her to be badass or whatnot, she's just a girl who's in love with Sonic. In Sonic the Comic however she's quite The Lancer to Sonic. She's far more lethal than any other version of her to date, and sports some Improbable Aiming Skills. Reflected in the games where, while still much more humble and goofy than in the comics, she is a Badass Normal whose Piko Piko Hammer makes her a key powerhouse in certain titles.
Speaking of Sonic, Antoine D'Coolette of Archie Comics' Sonic the Hedgehog series. In the Saturday Morning Sonic the Hedgehog series, he was a Cheese Eating Surrender Monkey who tend to let out a Girly Scream now and then and was pretty much The Load. This changed when issue 46 came out and he ended up dating Cyborg Bunnie Rabbot. By this point, he started growing braver and braver, becoming a competent swordsman, being tough enough to survive over a year in an Alternate Universe, slugging Evil Sonic unknowingly at one point and impressing his dying father enough that he gave his blessings for him and Bunnie to be married. Then he goes and nearly gets killed saving Prince Elias and his family.
The short In the Interim... from Issue #4 of My Little Pony: Friendship Is Magic (IDW) features Epic battle-damaged, trident-wielding Spike riding Celestia in the middle of the fight against the giant Cockatrice attack. And he ends up saving everyone!
Issue 7 in the main story has this to Spike as well.
And issue 8 does this to the citizens of Ponyville.
While H.P. Lovecraft's original Deep Ones were described as "degenerate fish-frogs" who have trouble moving around on land and are only a threat due to sheer numbers and relationship with bigger eldritch critters, Alan Moore's Neonomicon treats us to a seven-foot armored-skinned man-coelacanth with the physique of a bodybuilder who can pull down wrought iron gates and fight an entire SWAT team to a standstill single-handed.
The Transformers IDW: Has the Sweeps as this. The original Sweeps were just mooks and often ended up as Ineffectual Sympathetic Villains, here, they are still Mooks who go down en masse, but they're a lot more deadly, storming Kimia and killing most of the crew, even tearing one bot apart with their teeth.
Transformers: Last Stand of the Wreckers: Did this with Overlord, while he was always powerful, even back in Masterforce, here he's established as one of the most powerful cons period, having brought destruction to countless worlds.
Transformers: Robots In Disguise: Has this with Devastator, who was the biggest con to fall victim to The Worf Effect, even in his debut episode. In this series, he Took a Level in Badass, rampages through the city unopposed, and easily tears Superion in half. In the Dreamwave continuity he couldn't even land a hit on Superion, and only won because of the seekers.
Ares from Greek Mythology. Originally, he was portrayed as a bully who could only win against unaided mortals, got his butt kicked by anything supernatural, and was casually dismissed by fellow gods Zeus and Athena. Then the Romans came around and identified him with their god Mars, making him the patron god of Rome, second in importance only to Jupiter (the Roman version of Zeus), an ideal soldier, and an all-around badass. This might make him the Ur Example. In many modern adaptations, Ares is usually portrayed more in the style of Rome's Mars in order to make him an imposing and threatening character.
Satan tends to get upgraded from a fallen angel whose defeat is a given from day one and whose antics on earth are basically a bully picking on the teacher's pets to a full-blown God of Evil only kept from creating Hell on Earth by the forces of light remaining ever vigilant.
In the character's source series, Atop the Fourth Wall's The Entity (aka Missingno) is mildly creepy if you start applying Fridge Logic, somewhere between useful and annoying if you don't, and is nigh-universally pathetic in battle to the point of usually being incapable of victory. Now, he's a horror that makes other monsters look friendly and harmless, and reduces entire worlds to nothingness.
And according to Word of God, every other glitch Pokemon is just a different form of this version of Missingno.
In Death Battle, this trope applies to Harry Potter. Not that he was slacking in the book series, but in his fight with Luke Skywalker, he's capable of pulling off feats he canonically didn't.
In Pokémon Apokélypse, being a parody of darker and edgier works, everyone becomes awesome, especially Team Rocket.
In 2007 the CGSociety (for Creative Digital Artists) held a contest to create images and pieces using Greg Bear's book Eon as a reference point. The winning trailer was titled "Worlds Within Worlds". In it, the frant breaks a soldier's neck. In the book, frants are actually rather peaceful (they're useful due to their Hive Mind), and there's no danger at the moment in the book that the trailer portrays.