They both express the same thing, but there is a little bit difference between them:

We use petit à petit to describe a process/action which steps are evolving slowly but still they are clear and distinguishable ones:

• Petit à petit, l’oiseau fait son nid: This is a proverd and it means: little by little, the bird constructs its nest
• J’ai construit ma maison petit à petit: I have built my house little by little: The process of building, even if it is slow, involves clear and distinguisable steps.

We use peu à peu to describe a process/action which steps are evolving slowly but this process is not clear in that its steps are not distinguishable:

• Le climat se réchauffe peu à peu: the climate is warming little by little.