Assalamu alaykum warahmatuLLahi wabarakatuhu. Brothers how to understand this hadeeth?"Whenever Allah's Messenger (?) was given the choice of one of two matters, he would choose the easier of the two, as long as it was not sinful to do so, but if it was sinful to do so, he would not approach it ... (Bukhari 3560)"Is it permissible to choose hardest of the two options if it brings more benefit in wordly matters or religious matters?

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, sallallaahu`alayhi wa sallam, is His slave and messenger.

The Hadith indicates the permissibility of acting according to the easiest as long as it does not involve any sin. Acting according to the easiest is a matter of desirability, not obligatory. Al-Hafidh al-Iraqi said in Tarh al-Tathreeb: “The Hadeeth indicates that it is desirable to act according to the easiest and the most lenient as long as it is not forbidden. An-Nawawi  said: As long as it is not forbidden or disliked.” [End of quote]

It was reported on the authority of ‘Aa’ishah – who is the narrator of the Hadith mentioned in the question – that she completed the prayer during some journeys and did not shorten it. Some scholars said that she left the easiest and chose determination. Al-Hafiz Ibn Abd al-Barr  said in al-Istithkar: “She learned the shortening of prayers from the Prophet when he was given the choice to shorten or complete the prayer, he chose to shorten it, so that it would be easier for his nation, and she said: “Whenever The Messenger of Allah given the choice between two things, he chooses the easier of the two, as long as it was not sinful, so she herself acted without taking concession when it was permissible for her, in the ruling of choice that Allah had authorized.” [End of quote]

What can be concluded from her actions is that there is nothing wrong for a person to choose the hardest of the two matters for his own self, as long as it is permissible and without obliging people to do so.

Allah knows best.