Davening on Taanis Esther or Purim - Which is more mesugal, which the more auspicious time?

 In recent years there have been many advertisements and much promotion of the idea that the day of Purim is an especially auspicious time for prayer, with some even claiming or implying that one can daven then for anything with success guaranteed, whatever that means (one can daven to win the powerball lottery and be guaranteed to do so??).

Interestingly, though, I noticed this year something a bit different, being promoted by the Vaad Harabbanim charity organization recently. They are promoting Taanis Esther, rather than Purim, as the special day for davening. Below is an image of their poster promoting it. 

The passage of the sefer Kav Hayashar on which their poster is based, can be seen in context in that work here (starting with the top line of the page).

So which is it?

The Hassidic seforim seem to be promoting Purim day, while the Kav Hayashar is promoting the day before.

If I would have to pick one, I would take the latter.

Interesting.