How does Rasengan do so less damage? When Jiraiya used Rasengan on a tree, it shredded part of it and trees are not soft. They are so much harder than human flesh. However, the first time Jiraiya used it on a gangster, he didn't die.

Why is that? He should have been torn to shreds.
When the Rasengan makes impact, there are two effects that take place

The first effect is


  On contact, the Rasengan grinds into its target, propels them along the Rasengan's trajectory - either away from the user or into the ground beneath them


When Jiraiya used the Rasengan against the gangsters, this what we saw. 

The second effect is 


  and at some point bursts, causing severe damage at the point of contact.


The burst is what truly deals the damage. Jiraiya mastered the technique of the Rasengan and more than likely had control over it for it to not burst.

Anyways, he was trying to make a point and get the gangsters off of his back - there was no need to kill them. Jiraiya even says


  And I was holding back. You guys are hardly worth the trouble