I would say, it's really in the specific meaning a speaker wants to express. The words have an extremely close meaning, and in most cases can probably be exchanged. Обрадовать is a perfective aspect, and therefore, intuitively, it is applied when something has already happened or is expected to happen, and the fact of learning it brings joy. On the other hand, порадовать is an imperfective aspect, and carries exactly this meaning—of some process or action in progress. For example:
Ребёнок обрадовался мороженому (the child has enjoyed an ice-cream) vs. порадуй ребёнка, почитай ему (give a child some pleasure, read him a book).
The examples by Quassnoi give a perfect illustration of this distinction: each sentence has some hint of the time scale. Порадовать would relate to a landscape or a new watch collection which will last for some time. Неожиданно and спешу, to the contrary, emphasize the suddenness of the news.
So, to answer the OP, in that particular example the two words would be interchangeable, though the meaning would be exactly the same.
Давай, порадуй меня
assumes some process of telling me a good news; I will feel the pleasure for some time during and after being told.
Давай, обрадуй меня
assumes that right after having been told the good news, I'll be glad though this feeling may also be not really prolonged.