Well...I don't think both of them are horcruxes. Well basically...Dumbledore's theory was that Nagini is a horcrux and as she's sharing her soul with Voldemort's(acc. to Dumbledore) "Voldemort has extra-ordinary power over her even for a parselmouth"-Horcruxes, HBP.
So, if we are to believe what Dumbledore is implying over ere...that if u share your soul with a part of a soul which is created by murdering someone...in other words if u are the Horcrux then the person whose soul is in ur body has "extra-ordinary" control over you. As such...I haven't found any such extra ordinary control by Voldemort over Harry. (Since the books are from his POV we know that!) Also, don't you think that if Harry is the horcrux...his thoughts and his ability to be humane would be marred by Voldemort's soul residing in his body???
Don't you think Harry would be darker...and have evil thoughts. Also...don't forget..at the end of OotP, when Voldemort possesed Harry...it was sheer torture for Harry and when Harry thought about his love for Sirius...Voldemort found it unbearable to possess Harry and fled??? Also Harry described the experience as "He was in the coils of a large snake like creature.He didn't know where his body ended and where the creature's begun" It's not the exact quote but still if Harry had been the horcrux..he would have physically and mentally felt the effects of Voldemort's soul!
And like Dumbledore said...Harry's mysterious power AKA love is something unbearable and painful for Voldemort! So his soul could never rest peacefully in Harry's body! 😉
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