I agree! ♥ There's a lot of confusion with the two classes already, and that's my reasoning for bringing this up at all (so I apologize if I'm adding to it!)...because I fear adding Dragoon + Knight/Samurai might make the definition for Soldier hazy if there's not something else helping to define that team as well.
Personally, I see Agrias and Basch as kind of fitting more for the Dragoon + Knight category, even just in terms of their abilities in Tactics and RW respectively. They don't have nearly the same amount of healing or protective abilities like Cover that other Paladins such as Cecil, Beatrix, and Frimelda have...and I definitely see their personalities fitting more for the definition that you gave for Dragoons overall. While they're technically in military organizations, Basch tends to be more dedicated to one leader or cause (Ashe, and later Larsa) and Agrias is overall more loyal to Ovelia (even her reasoning for joining with Ramza's group is because she feels it is in Ovelia's best interest given what happens in the story, which is especially shown in the PSP version much later in the game). Both characters do things for the greater good, but they always consider the well-being of the people they feel they are protecting in the process too (sort of like Fang, actually!).
With Cecil, Beatrix, and Frimelda...I see them leaning more towards your definition for Soldier. Both Cecil and Beatrix are both in the military and are loyal to it (and feel conflicted when there is something in the military that goes against their viewpoints of what is right). More often than not, they want to do what they feel is for the greater good and will often sacrifice in their own ways something to achieve that (whether it be their personal beliefs or morals or even their positions in the military itself. With Beatrix, she even decided to go with Garnet because she viewed her as being more for the greater good despite her standing with the queen...and Cecil's whole story fits with that definition). There's not a ton of Paladin characters in the games, but I kind of view them as being more-or-less Soldier-y in how they approach things.
So, basically...my thoughts would be personally: Agrias and Basch are more Dragoon-like based off of your description and their abilities in game which aren't 100% as focused on Cover and healing others as most of the other Paladins are. Cecil and Beatrix...I'd lean more towards Soldier, just given how their stories play out and their actual abilities in game that lean more towards the Soldier definition (and, randomly, I've always considered Beatrix a Soldier and often use her for Soldier votes...and I know at least one other person on our team has done the same. So maybe that's just more of my personal bias talking, lolz).
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Personally, I see Agrias and Basch as kind of fitting more for the Dragoon + Knight category, even just in terms of their abilities in Tactics and RW respectively. They don't have nearly the same amount of healing or protective abilities like Cover that other Paladins such as Cecil, Beatrix, and Frimelda have...and I definitely see their personalities fitting more for the definition that you gave for Dragoons overall. While they're technically in military organizations, Basch tends to be more dedicated to one leader or cause (Ashe, and later Larsa) and Agrias is overall more loyal to Ovelia (even her reasoning for joining with Ramza's group is because she feels it is in Ovelia's best interest given what happens in the story, which is especially shown in the PSP version much later in the game). Both characters do things for the greater good, but they always consider the well-being of the people they feel they are protecting in the process too (sort of like Fang, actually!).
With Cecil, Beatrix, and Frimelda...I see them leaning more towards your definition for Soldier. Both Cecil and Beatrix are both in the military and are loyal to it (and feel conflicted when there is something in the military that goes against their viewpoints of what is right). More often than not, they want to do what they feel is for the greater good and will often sacrifice in their own ways something to achieve that (whether it be their personal beliefs or morals or even their positions in the military itself. With Beatrix, she even decided to go with Garnet because she viewed her as being more for the greater good despite her standing with the queen...and Cecil's whole story fits with that definition). There's not a ton of Paladin characters in the games, but I kind of view them as being more-or-less Soldier-y in how they approach things.
So, basically...my thoughts would be personally: Agrias and Basch are more Dragoon-like based off of your description and their abilities in game which aren't 100% as focused on Cover and healing others as most of the other Paladins are. Cecil and Beatrix...I'd lean more towards Soldier, just given how their stories play out and their actual abilities in game that lean more towards the Soldier definition (and, randomly, I've always considered Beatrix a Soldier and often use her for Soldier votes...and I know at least one other person on our team has done the same. So maybe that's just more of my personal bias talking, lolz).