It's to do with formality. Subject pronouns are more formal than object pronouns here. But if you really want to be formal, then be consistent: He is stronger than he is, and make it understandable: Peter is stronger than Tom (is).
He is stronger than him and He is stronger than he (is) are both ok, the problem is that without a picture or a context it is difficult to understand and differentiate He from him. To avoid it I suggested Peter is stronger than Tom (is), that is, or Peter is stronger than him or he (is) or He is stronger than Tom (is).
In the following sentences, formal usage requires the subjective case (I, he, she, we, they) because the pronoun would be the subject if a verb were supplied:
You are more responsible than he. (in full, ...than he is.)
Informal usage permits the objective case:
You are more responsible than him.
Formal English uses the objective case (me, him, her, us, them) only when the pronoun would be the object if a verb were supplied:
I thought you preferred John to Mary, but now I see that you like her more than him. (which means ...you like her more than you like him).
Just watch out what you really want to say:
Martha and Jason like spending free time with eath other. I like spending free time with them too. However, Martha spends more time with him than me. (Martha doesn't spend as much free time with me as she does with Jason.) or (Compared with Martha, I spend less free time with Jason.) AMBIGUOUS
However, Martha spends more time with him than I (do). (Compared with Martha, I spend less free time with Jason.) UNAMBIGUOUS
So, if I get you right 'she loves me more than you' may mean:
1- She loves me more than she loves you, or
2- She loves me more than you love me.
It's all very well with I/me, he/his... but what about 'YOU' --> AMBIGUOUS unless you provide DO? is it so?