All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
We do not understand what you mean by your question: "Is there a difference between the first and the second Istikhaarah prayer?" It is known that your first Istikhaarah is different from the second one as far as the working place is concerned.
However, as long as you have performed the Istikhaarah prayer seeking the guidance of Allaah in regard to either continuing your work in Qatar or to work in Saudi Arabia, then Allaah will decree what is more suitable for you.
Finally, it is permissible for you to seek the advice of sincere and trustworthy people whom you trust. You should not hesitate after praying Istikhaarah and seeking advice.
May Allaah guide you to what is good for you.
Allaah Knows best.