What is more important in Kaliyuga? Following dharma or surrendering dharma?

Following Dharma – specifically, Bhagavata Dharma.
What is Bhagavata Dharma? Reading Itihasas and Puranas, listening to them and performing Nama Kirtan always. These are the essentials of Bhagavata Dharma.
The Vedas speak about Dharma. The Bhagavata Dharma is verily the nuance of Dharma (‘Dharma Sookshma’). It is not only a revolutionary dharma, but also the most practical one.

With the growth of modern technology, each nation tries to compete the other in terms of scientific discoveries. Then, where is the chance of knowing the Almighty and increasing our devotion for Him?

As long as a fetus grows in a womb normally, everything is happy and peaceful. But if the child continues to grow in the womb even after 10 months, it is not peaceful anymore. It is rather alarming and dangerous isn’t it? Similarly, the growth of science and discoveries in this field are good only to a certain extent. Beyond that it becomes dangerous, and the world will be fed up with the troubles that these cause, rather than enjoy its benefits. If not now, at least then, the world will realize the presence of the supreme power called Sri Krishna.

Why do we have crime and injustice in the world?

That is the nature of the Kali Yuga. The state of the current yuga has been predicted long back by our Maharshis in the various spiritual texts of our Dharma. We cannot avoid that. The only way out is to try to remain unaffected by it, by holding to the Feet of the Lord.
The simplest way towards this goal is by chanting the Mahamantra.