The titular characters of Miraculous: Tales of Ladybug & Cat Noir have proven to be impeccable heroes, solidifying their iconic alter egos with their respective Miraculous. Marinette Dupain-Cheng brings Ladybug's powers to their full potential with her creativity and quick-thinking while Adrien Agreste wields Cat Noir's destructive powers with skill and practiced ease. The two balance each other out well with the Ladybug and Cat Miraculous often being alluded to as yin and yang.
But in Season 3, Episode 5 "Reflekdoll," Ladybug and Cat Noir switch Miraculous to become gender-swapped variants of each other's superhero identities: Mister Bug and Lady Noire. And it is during this swap that we are shown that the two are not on an equal playing field. In fact, being Ladybug is much harder than being Cat Noir.
When Juleka Couffaine is akumatized by Hawk Moth and given a sentimonster to control by Mayura (Nathalie Sancoeur, holder of the Peacock Miraculous), she becomes the supervillain "Reflekta." Introduced in Season 1, Reflekta has the ability to change people's appearances and turn them into an exact copy of herself. In the Season 3 episode, as she wreaks havoc on Paris, Marinette and Adrien are struck by her powers. As a result, their Kwamis (Tikki and Plagg), who were lost earlier in the episode, cannot easily identify their owners. As the situation worsens, Plagg runs into Marinette and she takes the Cat Miraculous to save time, leaving the Ladybug Miraculous to Adrien.
While Lady Noire adapts to her new powers and gadgets fairly easily, Mister Bug has a bit more trouble, facing a steep learning curve to use the Ladybug yo-yo and its unique abilities. He also overestimates the power of the Lucky Charm as the purpose of the object it provides is never straightforward. Mister Bug learns the hard way that the Ladybug's powers call for a lot more analytical and problem-solving skills than he is used to. Additionally, he uses his Lucky Charm too early into the battle, giving him a time limit to defeat Reflekta before he transforms back.
On top of that, he bears the responsibility of capturing the akumatized butterfly and setting it free, not to mention the prospect of releasing the magical ladybugs that repair any damage caused during their battle. Both of which Lady Noire has to remind Mister Bug to execute. These tasks are not only necessary in saving the akumatized victim, but in restoring Paris and others who got caught in the crossfire. As such, Ladybug's powers are crucial to both win the fight and save lives.
On the other hand, Lady Noire doesn't encounter such difficulties. When she uses her Cataclysm against the sentimonster, it fails to destroy the giant robot. Instead, it goes out of control, creating further chaos. However, Adrien has never used his Cataclysm against a sentimonster before so neither could've predicted this outcome, suggesting that Adrien would have made the same mistake. With that hiccup accounted for, Lady Noire is pretty much a natural with the Cat Miraculous's powers.
To Adrien's own admission, being Ladybug comes with a greater responsibility than Cat Noir, underscoring why it's Ladybug's name that's more prominent in the show's title. This is also confirmed by Thomas Astruc, series creator and director, who responded to a fan's complaint over Marinette's lack of struggle with the Cat Miraculous on Twitter: "That was the whole point of the episode. Showing that the Ladybug is [a] huge burden compared to the Cat Noir part."
That being said, it's safe to presume that the lesser burden on Cat Noir's shoulders contributes to his carefree nature in comparison to Ladybug, who takes things a bit more seriously in Miraculous. Despite "Reflekdoll" highlighting the importance of Ladybug, it's also worth mentioning that Cat Noir is a worthy partner who never fails to have Ladybug's back in the worst of situations. He always assists her in carrying out her plans, effectively creating the team dynamic that they are known for. Though playing a smaller role, Cat Noir still plays a vital part in the long-running battle against the supervillain Hawk Moth.