Prince of Wolf (2016)

Maria, struggling financially, juggles a low-paying day job with nighttime shifts at a cabaret to fund her sister Nana's eye operation. Tragedy struck their family when a young Maria accidentally caused a fire, resulting in Nana's blindness and their father's death. Shiro, a discontented concert pianist, crosses paths with Maria in a traffic accident, leading to his hospitalization. Adopting a false identity and amnesia, Shiro seeks refuge at Maria's home, eventually becoming a cabaret pianist. Unbeknownst to them, fate weaves a complex web, revealing that their lives were never meant to intersect.

Both male leads develop powers from animals and try to fight against the modern world but realise they need to accept the duality of both worlds in harmony and balance.

from what I read on synopsis, both series has similiar stories. about a guy raised in a wild forest, and brought to the city by the girl.

Different country but the storyline is actually quite similar! Both leads are rich (hot) heirs but have 'something' that happen to them and their families try to search for them. Both dramas have an ajusshi who wants to prevent the leads from meeting their families. Both dramas have the lead guy fall in love with a country-side girl early in the series. Both series have the leading girl help the lead guy adjust to the new environments. Both dramas have super cute romance/ comedy scenes.

The story of a little boy who got lost in the forest when he was young and raised by the wolves, his paths crossed with a woman who's an amateur photographer who decides to go to Mountain to take pictures of the landscape, he saves her and takes her to his cave thinking that she's his female wolf mate. She takes him from wild world to Civilised World back to his parents.

Similarities: Prince of Wolf deals with a human raised by wolves who has enhanced strength and senses, and is misjudged by other people (at least initially).
Gu Family Book deals with a half human/half gumiho (fox demon) who has special powers and is treated like a monster by everyone who finds out about his true identity.
Both kinda deal with other people freaking out about their wolf/fox demon rage issues, and have a female lead who understands their true nature.
Differences: Gu Family Book is a Korean Drama, and is set in a historical setting. MC is not as "innocent"? (father of the MC is though).

Both leads were raised by wolves. In "The sound of the desert", Jin Yu (Cecilia Liu), an orphan girl of Xiongnu ethnicity, was raised by wolves in the desert, until a Han Chinese decided to adopt her.

Similar concepts where male leads were raised by wolves since a very young age. They had no contact with the outside world until they meet the female leads

Both male leads act like dogs/puppies. This one is more like Tarzan though.
Older woman/younger man age gap

-ML who doesn't know anything about human relationships and learns about them through FL
-ML is convinced FL is a special existence to him and is mesmerized by the FL
-ML is in their particular predicament because of someone's greed.
Differences:
Puppet prince has a more darker and more tragic plot whereas Prince of wolf has a lighter, fluffier plot