I don't remember Nina transforming in BoF1 in battle, do you mean the bird transformation outside of battle?
Yes, that's what I meant. Nina loses the ability to transform into the great bird in the other games since everyone after the first game is no longer pure blooded. Although Ryu can still technically transform into a dragon in the other games, it's still not quite the same. In Breath of Fire 2, he uses up all his AP for one powerful attack. Whereas, in the first game, he can stay transformed into a dragon thoughout the entire battle, dealing tons of damage each turn (especially with Agni - 999 damage per turn). So in other words, the Breath of Fire 1 characters are better than the ones in the other games.
Ryu in the first game for example would easily beat the ones from the other games using his dragon transformations. He might even be a better swordsman than the other ones as well. Ox also seems stronger than Rand (being able to shake trees by punching them as well as the ability to move heavy objects thoughout the game). Nina is more useful as a healer/fighter than a mage and Karn is the only actual human you get to use in the whole Breath of Fire series as far as I remember. Not to mention the fact that his fusions are better than the shaman ones in the second game which defuse when a character is low on HP or during certain cutscenes.
Being able to swap out characters any time, even during battle was also an original and useful perk. I don't understand why Ryu can't transform into Agni when Karn and the others are fused, but whatever. Being able to run a store with Gobi was pretty original as well for an RPG during the time. I believe that's how you get Ox and Nina's best weapons. And last, but not least, saving at the Dragon Lord temples in the first game was quicker and more convenient than having to use the churches in the second game, since not every town has a dragon shrine. It's also pretty ironic since they're considered to be enemies that worship a false demon god.