All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
If the aim behind such a competition is to encourage the competitors to learn the Quran by heart and to recite it in the best way possible, then there is no harm in holding these competitions regardless of whether the participants get prizes or not, provided the prize itself is from lawful sources, i.e. not ill-gotten money taken from Riba or Gambling, … etc., and provided that such competitions do not become a source of hatred and misunderstanding between the competitors themselves.
Allah knows best.