Each person in the Trinity has the same qualities as God because they are each fully God; no other member is less God than the other. Because God is uncreated and has always existed, this also applies to them.
Before the idea was made dogma at the First Council of Nicaea, there were also other ideas about the nature of God. These included:
That Jesus wasn't a human at all; his human form was nothing but an illusion (Docetism).
They are three distinct gods who worked as a team to form one Godhead (Tritheism).
The Father, Son, and Holy Spirit are not three distinct persons but are only different names for the same being (God), and each is a manifestation of God (Modalism).
God the Father is the only person of the Trinity who is fully God; the Son and Holy Spirit weren't fully God, and they had a beginning (Subordinationism).
God the Father is the only true God; the Son had a beginning, so he wasn't God; and the Holy Spirit is not a person (Arianism).