Verb To Be

[beachboy]

Both Are Good Students, But I Believe John Is The Better.
Both Are Good Students, But I Believe John To Be The Better.

Are Both Grammatically Correct?
Is So, Why Does It Happen In This Case? Could You Possible Give Me Another Example In Which It Happens? Thanks A Lot

 

[Anglika]

Yes, both are correct.

The second sentence is the present subjunctive form.

I asked that it be done yesterday

 

[beachboy]

I mean, I was looking for other examples in which it´s possible to use either "is" or "to be"

I think/guess/hope/suppose John is (to be) the better of the two
I think/guess/hope/suppose it is (to be) easy to play the piano