to be fair, even at the beginning, Strange was set up to be more emphatic and caring than Tony inherently due to being a doctor.
Huh? Act 1 Strange was far more of a giant, unempathic asshole than Tony ever was, specifically due to the type of doctor he was.
! Strange outright refuses to treat difficult patients that might stain his "perfect record", choosing only ones "worthy of his talents", which may make him look good. He is clearly more invested in his legacy, doing talks and having procedures named after him than actually saving lives. This type of Doctor absolutely exists; I've met and known several people who became doctors because the pay and prestige is great, and their grades are so good that "might as well". Over the course of the movie Strange learns to appreciate the true value of being a Doctor (helping others, not killing people), and leaves actual doctoring behind altogether in order to protect even more people.
! It's the ego and arrogance that drive home the parallels. For all we know, in future films, we'll see Dtrange being the arrrogant jerk to those in the Universe who doesn't understand magic and trying to wield its power just like he was a smug jerk to Nick for not being as good of a surgeon. Mind you, he's still in training at this point and has much to learn.
! And in the end Strange hands over Nick the scalpel, lets him do the operation, and abandons the profession that defined his entire identity. Wong, Mordo and the ancient one constantly belittle and dismantle his arrogance. And he DOESN'T GET THE GIRL. The girl leaves him in the hospital to go do her job, because life isn't about you, Strange. From where he starts in the movie Strange loses pretty much everything that defines him: his hands, his profession, his closest relation, and is left alone in the sactum, and unseeen and unknown protector of the world. Tony has Peppet Potts, worldwide fame and luxury, and publically flies around in his awesome Iron Man suit, because he loves doing it. Dr. Strange would have a thing or two to tell Tony Stark about growing up.
! And while he's cognizant of the dangers that too much power can have in a way Tony seems blinded by (as shown when returning the Eye back to its original place) he's still holds that mad scientist / can do no wrong attitude when he decided to mess with the Laws of nature because he seemed it necessary. He never even acknowledges that Mordo probably made good points at the end about how messing with the laws of nature causes it's fair share of evil (like Vision pointed out, which I'm guessing is a Phase 3 trend?) Bet the question would be if prepping to stop beings like Thanos is worth having the superheroes do what they do.
! I think its unfair to call it "mad science/can do no wrong" attitude. Strange manipulating time to trick Dormammu and restore and reverse Kaecelius' damage is far more reasoned and defensible than Tony Stark building another super-robot and crossing his fingers that "it'll probably work this time. We're mad scientists bro!". Plus, him returning the eye also means that purposefully lets his watch and hands stay broken, as a reminder to himself, as he stands alone in his sanctum.
I fully agree that theres similarities to be found between Strange and Tony, but I think they develop and end up decidedly different. Ultimately, I think Stranges development is just greater than Tonys (partially because Strange starts off as an asshole), and that he actually sacrifices something.