And now for an oversized spoilerrific review...In other words don't read ahead if you wanna have it all ruined XD
I think it's an issue of the manga being better told than the anime for starters - the manga was basically using Hideki and Chii as foils for stories about various man/machine relationships, not just a silly fanservice show like the anime was for the most part, - and also an issue of what constitutes a good person between the two cultures - Chii was kawaii in the full connotation of the word; she wasn't just cute, she was also somewhat domestically talented and well-mannered. In the western context, that's kinda no big deal, but if I've got my cultural info straight, it counts a considerable bit more in Japan.
The big note is that in the manga it's clearly delineated that Hideki can't have sex with Chii, so the love has to be that of genuine nature. In a sense, it's basically a way of working with the last man-machine parable could be tackled by Chobits, which is can you a machine as a person, not as a walking talking sex-toy? Hideki says yes, he can. In a sense, it doesn't even seem that weird given that are people, families even, out there who have bought Real Dolls and proceeded to treat them very similarly to Persocoms: purchasing them complete outfits, having picnics in the backyard with them, sitting them with the rest of the family at dinner. If people are willing to treat objects that only look fairly human as human, you only need about as much personality as Chii before someone goes head over heels. CLAMP is closer to reality than they may even realize with Chobits.