The difference may be because it wasn’t an intentional Horcrux.
When Horcruxes are created from inanimate objects, it’s intentional, and the wizard creating them has to actually do something (though we don’t know what) to seal the piece of soul in the object.
With Harry, the Dark Lord took no intentional action to put a piece of his soul in Harry. It’s therefore possible that the soul piece, of its own accord, chose to “possess” a living thing rather than an inanimate object.
It certainly seems to be easier for soul pieces to possess living things than inanimate objects. Even the soul pieces in the inanimate intentional Horcruxes can possess people temporarily, though they’re dependent on the objects for survival.
“And once the diary was properly destroyed, the bit of soul trapped in it could no longer exist. Ginny tried to get rid of the diary before you did, flushing it away, but, obviously, it came back good as new.’
‘Hang on,’ said Ron, frowning. ‘The bit of soul in that diary was possessing Ginny, wasn’t it? How does that work, then?’
‘While the magical container is still intact, the bit of soul inside it can flit in and out of someone if they get too close to the object.”