Chess Puzzle of the Week (137)

This week, one of my favourite subjects: king and pawn endings.

White to play. I want you to analyse two moves (you can, if you want, analyse any number up to 10, but these are the two moves I’m interested in).

a) Kd3

b) Kf3

Do you have a preference, or are they both the same? Do either, or both, of them win, draw or lose?