Core Theme Two scythe-wielding leaders lost their mothers in childhood and constantly strive to emulate them; even when they fall, they always rise again to fight.

Connections:

Both Ruby Rose and Cole are scythe wielders (Ruby with Crescent Rose and Cole with the Scythe of Quakes).

Both use spiritual energy (Cole's Spinjitzu and Ruby's aura).

Both had legendary warrior mothers who passed away, and both inherited rare powers tied to them:

Ruby inherited the Silver Eyes from Summer Rose. Cole inherited the Elemental Power of Earth from Lilly 

Both Cole and Ruby lost their mothers in childhood, and both want to be like her and emulate her. Ruby wants to be like her mother and the heroes whose stories she read. Cole made a promise to his mother that he would always fight the villains.

After their mother's death, this will cause sadness to people close to them (Lou  Cole's father and Qrow  Ruby's uncle and Tai Ruby's father).

Both served as leaders of their teams:

Ruby is the leader of Team RWBY.

Cole was the leader of the Ninja before Lloyd took that role.

Both have arrogant teammates they clashed with upon first meeting:

Weiss for Ruby.

Kai for Cole.

Both have robotic companions (Penny for Ruby Zane for Cole.)

Both will be heartbroken after losing important friends in their lives (Pyrrha and Penny with Ruby because of Cinder, and Zane in season three because of the Overlord for Cole).

Both have comedic teammates they later end up clashing with:

Ruby with Jaune (Volume 9).

Cole with Jay (mainly due to their rivalry over Nya).

Both participated in major tournaments featuring other users of powers similar to theirs:

Cole participated in the Tournament of Elements (both the original and the Dragon Rising version), featuring other Elemental Masters.

Ruby participated in the Vytal Festival, featuring other Aura users.

Both of these tournaments were also celebrations:

The second Tournament of Elements celebrated the Source Dragons.

The Vytal Festival celebrated the end of the Great War.

Both have wise white-haired mentors who hide massive secrets:

Master Wu

Professor Ozpin

Both of them, after meeting their teachers, will leave their original academy (Cole, after escaping from Marty Oppenheimer School of Performing Arts, will meet Wu and become his student; Ruby Rose, after meeting Ozpin, will leave Signal Academy and join Beacon).

Both mentors feel guilt because someone close to them became a great villain:

Garmadon for Wu

 Salem for Ozpin

Both mentors also return in younger forms after a major event:

Ozpin reincarnates through Oscar.

Wu disappears through time and later returns as a baby.

Both have half-animal allies from races that suffer discrimination:

 Blake (a Faunus)

Skales and Frak (a Serpentine)

Both once served under extremist leaders:

Blake under Adam.

Skales under Pythor.

Frak under Lord Ras

Both have close teammates with evil  fathers:

Weiss with Jacques Schnee.

 Lloyd with Lord Garmadon.

Both of these people wanted to be like their father or gain his approval, but in the end, this became their greatest fear (Weiss because she wanted to be the best heir to the Schnee family name, and Lloyd because he wanted to be evil like his father).

Both temporarily transformed into something non-human and nearly lost themselves forever:

Cole became a ghost and risked being trapped forever in the Temple of Airjitzu.

 Ruby transformed into wood in the Ever After and risked being trapped there forever.

Both were manipulated by mysterious villains they encountered there:

Master Yang manipulated Cole.

The Curious Cat manipulated Ruby.

Both of them have been trapped with a group of people in a strange world after a major event (Ruby in Ever After with the rest of the RWBY team and Cole in Land of Lost Things with The Finders after The Merge).

Both will fall into darkness (Ruby after drinking the magic tea in V9 and Cole after falling in Season 10). Both their teammates think they're gone, but they'll be shocked by their return.

Both have impulsive fiery companions:

Yang for Ruby

Kai for Cole

Both love sweets:

Ruby loves cookies.

Cole loves cake.

Both hid personal struggles from their teams:

Ruby often hid her emotions and inner pain.

Cole hid the truth about his father being a dancer and their strained relationship.

Later, both learn to open up and become more emotionally honest.

Both have strong moon symbolism:

 Ruby is heavily associated with the shattered moon and its appearance in the RWBY Red Trailer.

Cole is connected to moon imagery in Ninjago, especially in Day of the Departed.

Both fight magical main antagonists:

Salem

The Skull Sorcerer

Both villains can summon dark creatures to aid them.

Both possess unique special abilities:

Ruby’s Silver Eyes

Cole’s Spinjitzu Burst

These are ancient inherited powers tied to their lineage.

Both wield transforming weapons:

Crescent Rose transforms into a sniper rifle.

 The Scythe of Quakes transforms into a vehicle.

Both eventually suffer emotional breakdowns:

Ruby in Volume 9 due to repeated failures and crushing expectations.

 Cole in Ninjago Season 13 due to his inability to use Spinjitzu Burst.

Despite this, both rise again and continue fighting.

Both battled evil sorceresses connected to their mentors’ pasts:

Salem

Aspheera

Both temporarily led separate teams after splitting from their original group:

 Cole led the resistance in Shintaro The Upply.

 Ruby led Team RNJR after being separated from Team RWBY.

Both befriend small animal companions in strange alternate worlds:

 Little in the Ever After.

 Adam the spider in Shintaro’s dungeons.

Both wield powers connected to godlike figures in their worlds:

Ruby’s Silver Eyes are tied to the God of Light.

 Cole’s Scythe of Quakes is one of the Four Golden Weapons created by the First Spinjitzu Master.

Both men lost their training grounds. Ruby lost the Beacon Academy in the Beacon Fall event.

 Cole lost the Monastery of Spinjitzu when it was burned in the first season. He will return later, but the Monastery of Spinjitzu was lost for a period of time before his return.

Both struggle with feelings of failure when they believe they cannot live up to their mothers’ legacy, but ultimately learn self-acceptance.

At their core, both of their journeys are about legacy, self-worth, and learning to accept who they are.

The contrasts: 

Cole is the oldest and most level-headed ninja, while Ruby is the youngest and most playful.

Cole's father, Lou, didn't initially support him and didn't want him to become a ninja, unlike Tai, Ruby's father, who was supportive of her.

 Also, Ruby isn't as good a dancer as Cole (something I wanted to mention for Some reason).

Fighting Potential 

A battle between them using a scythe would be spectacular. Ruby could use her special ability to dodge Cole's attacks and utilize Dust to gain various powers, while Cole could unleash his Dragon Form. The climax would be epic, featuring Ruby using her Silver Eyes and Cole unleashing his Spinjitzu Burst.

Music Potential

 Blending the epic rock style of Ninjago with the orchestral music of RWBY would create a truly amazing, high-energy mix.

Cole VS Ruby Rose (Ninjago VS RWBY)