The two are interchangeable in British English, although some people feel that the use of 'as yet' is rather verbose (uses more words than necessary).
There is AS YET no prospect of the return of peace. Correct
There is yet no prospect of the return of peace. This doesn't work with the 'yet' in this position
There is no prospect of the return of peace yet. Correct
There is not yet a prospect of the return of peace. Correct, but rather clumsy - I recommend using sentence 1, 2, or 3.
There is not as yet a prospect of the return of peace. Correct
He booked for today, but he hasn't checked in as yet. Correct
He booked for today, but he hasn't checked in yet. Correct