The primary reason why Asuras pray to Brahma or Shiva is to gain power through the virtue of boons obtained by them. This is clear from many cases where Asuras did penance to Brahma/Shiva to obtain boons.
In Ramayana Ravana became invincible to gods and demons due to boon obtained from Brahma after performing penance of thousands of years. Even his sons Indrajit and Atikaya rose to power after praying to Brahma and obtaining boons. Tripura demons and Hirankashyap became a powerful being due to Brahma,’ s boon of virtually being indestructible by tormenting himself through austerities. Even asuras like Mahishasura and Hiranyaksh became powerful as a result of Brahma,’ s boon as per puranas.
When we come to Lord Shiva we see him granting boons to evil in Mahabharata. The likes of Jydratha and Jarasandha obtained boons from Shiva after worshipping him such that Jarasandha was able to defeat all the kings and Jyadratha managed to stop 4 Pandavas except Arjuna on 13th day.