Do they have similar meanings?

'More effectively' is not appropriate for musical ability.

Hi Mister Micawber,
Thank you for your help.
What about, 'in a more excellent way than'?

TS

Not natural at all.

Hi Mister Micawber,
Thank you for your reply.
And this one, 'to a greater degree than'?

TS

No, these are all awkward or inappropriate paraphrases of what is a perfectly good sentence as it stands:

He plays the piano better than his father.

If you must do this, go to a different but natural casting:

He is a more accomplished pianist than his father.

Mister MicawberHe is a more accomplished pianist than his father.

Hi Mister Micawber,
Thank you for your help.
The thing is I'm trying to find another sentence similar to the one given below for a True or False exercise.
He is only six years old, but he plays the piano very well. In fact, he plays it better than his fath

He plays the piano more proficiently than his father.
He plays the piano more skillfully than his father.

Also:

His piano skill exceeds that of his father.
As a pianist, he is more proficient/skilled/accomplished than his father.
Playing the piano, he proves more proficient than his father.

screamererHis piano skill exceeds that of his father.

Playing the piano, he proves more proficient than his father.

These are not natural.

Hi screamerer,
Thank you for your examples.

TS