In the first passage Hananiah, Mishael, and Azariah are characterized as yielding up their bodies so as not to serve any god. In the second Darius states that Daniel serves God constantly. That is validated by the context. The satraps knew that they could trap Daniel in worship of God.
Those are amazing things to be said of someone. Devotion to God is more important than life and being known by all as serving God constantly.
Paul had a similar attitude in Philippians 1:21; 3:7 – 16; and 1 Corinthians 9:15 – 27.
I do not know many, if in fact any, of which I can say those things about. However, that seems to be the assignment. To what else are we to give our lives that is better?