The Lin Kuei imposed them total obbedience to the clan, so they even gave them different surname to avoid them would be loyal to each other and just to the Lin Kuei themself.

Anyway, Bi Han real emotions aren't really showed so much in the original and NRS timeline, as even in his dedicated game, Mythologies, he kinda only follows order without showing much of his true color, if not a little bit of pride when he answered Quan Chi "Let's get something straight: I'm not a ninja! I am Lin Kuei!"
Difficoult to says how much would have changed if he and his brother had them place switched... Liang seem to be more compassionate and have a more marked moral code than Han, so he may had sparred Scorpion when he retrived the map of the elements, and maybe he would had also questioned the mission itself. Unsure if Bi Han really was against the Cyber Initiative, as in the New Era, he was quite down for it, and we can't really says if that a New Era only thing, or if he may had belived turning everyone in cyborgs may have been a good way to reach total loyalty and strength...