The difference is "straightforward or not"
私が好き？ ： Do you love me?
Why does she(*) ask this question ?
It is because she is not sure that he loves her.
Then 私が好き？ is too straightforward or, like, needs too much commitment, or, like a final question.
Instead she would ask 「私のこと、好き？」
If I translate it into a strange English,
"*Do you love 'about' me?"
That would be a little softer.
* When you say 「私が好き？」 , this 私 is, for 99.9%, a female.
Google it with "私のこと、好き？" and you will find it.
People don't say 「私のことを、好き？」 . They always say 「私のこと、好き？」
Google it with 「私のことを、好き？」
and you will see the results only for 「私のこと、好き？」 .