OK guys, just to the point about the similarity between them. I mean just about the character, not the plot.
Ash Lynx x Squall Leonhart
Both of them have some cold face and manner, and also anti-social (Squall is really anti-social eventhough he is a SeeD's member, while Ash actually isn't so-so. He has his own gang, just he can't trust anyone carelessly because of his struggle with the world he endured and his past), but actually they are the gentle and kindhearted behind their cold manner. Also, both of them have their own love interests who can melt their cold-hearted.
From the meaning of name, both of them have the names that mean a "lion". Ash's real name, Aslan in the turkish is lion. Meanwhile, Squall's last name, Leonhart, is a variation of the English surname "Lionheart". Lion Heart means to possess or display courage, being able to face and deal with danger or fear without flinching. Even he has some accessories that form of the lion.
And the last but not least is....
Believe or not, both of them (especially manga!Ash and Squall in the original game) being designed based on River Phoenix by their own respective character designers, Akimi Yoshida (Ash) and Tetsuya Nomura (Squall). Ash's design by Phoenix can be seen after the Volume 06 and so on even his (spoiler) ending. Meanwhile, Squall's resemblance with Phoenix not only just his appearances especially his hairstyle, but his birthday is the same with the latter, August 23rd. Don't forget, both of them is 17 years old.
Ah, almost forget, both of them have their own weapon. Ash has dagger and gun, while Squall has gunblade. Even i think gunblade is the combination of dagger and gun, like Ash has to make it efficient maybe, LOL!
Eiji Okumura x Rinoa Heartilly
Despite of their different genders, but both of them share the same traits: compassionate, warm, and friendly, although they can act stubborn and naive. I mean, they are the same, despite of their differences by the age (Eiji is 19 while Rinoa is the same with Ash and Squall). Also, they have little experience with the realities of combat in their own harsh worlds (Eiji tries to help Ash discovers about Banana Fish and save Ash eventhough he didn't have some experiences about fighting and guns, while Rinoa joins a resistance movement fighting Galbadia to achieve Timber's independence in a mixture of genuine desire to fight for Timber and rebellion against her father). Both of them can be impulsive and act without thinking, which gets them into troubles but they are loyal to their own friends and committed to doing what they think are right.
Like yin and yang, both of them have some dark color appearances than their contrast partners. While Ash and Squall have light-colored eyes and hair, Eiji and Rinoa have black hair and dark brown eyes. Even their eye colors reflect some warm and calm manner from the owners.To support their warm personalities, they have the angelic face, especially their smiles.
Both of them can be depicted as someone who can fly. Eiji eventhough not really can fly, but at least he can do pole vaulting which help him run away from Marvin's and Frederick's goons, also report the location of their hostage place, then Ash constantly mentioning him being able to fly. His sweater from the first episode and his phone case also have birds on them. Meanwhile, Rinoa is known for her trademark "angel wings" printed on the back of her duster sweater and, as such, her "character symbol" is a white feather that signifies the wings. Even when she activates her limit break "Angel Wing", her trademark can change to be the real corporeal wings that lift her off the ground.
Also, both of them have the pet dog as their companion. Rinoa has Angelo, an Australian Shepherd dog who accompany her during her battle even his can be use as her weapon (i don't how can he can be the cannon by the owner, Lol!) while Eiji has Buddy, a Golden Retriever dog. But Eiji just has it in the epilogue of Banana Fish, Garden of Light and New York Sense. Both Angelo and Buddy are seem like the good dogs based on their appearances, just like their owners.
Updated: Pardon for me, actually Angelo is a female dog, not male despite her name seems masculine. I checked it in final fantasy fandom that Rinoa's dog is a female.
Frederick Arthur x Seifer Almasy
Both of them are the rivals of the respective main protagonists, but they aren't the important main antagonists (the real main antagonists are Dino F. Golzine for Banana Fish and Ultimecia for Final Fantasy VIII).
Both of them have the blonde hair and cold and cruel icy blue eyes. They look more masculine than their own rivals maybe.
Both of them have their own hatred toward Ash and Squall inspite they share same group. Arthur hates Ash because he always loses from Ash after fighting and fails to be the leader of the gangs. Meanwhile Seifer rivals with Squall when battles with him to prove their superiority in SeeD. Then they choose to betray them through they join with the main antagonists. Arthur allies with Dino to get his position as the leader of the gangs in Manhattan in a cheating way, while Seifer choose to loyal to Sorceress but i don't for what because i don't know much about him and his story by the way. But he seems like he still cares with SeeD with his own way. Then i think Seifer is better than Arthur. Then both of them can be likeable antagonists.
So, that's my thought about the similarities of Banana Fish with Final Fantasy VIII. I hope someone makes fanarts about them, either crossover fanart or BF characters cosplay as FF 8.
Some additional note, Squall's biological dad, Laguna Loire, shares same voice with Max Lobo, eventhough his looks and combat with gun seems like Blanca. That means, Laguna is the combination of Max and Blanca, the ideal typical of Ash's dad. LOL!