Are Buddhists supposed to feel superior compared to other people, and to brag about it?
What you are noticing is a familiar behavioural pattern unearthed by various Buddhists practices. In Tibetan and Theravada Buddhism it is called Māna or to use the more user-friendly term: conceit. Theravada sees this as one of the very last fetters to fall away. Conceit can be quite a horrible one. I have experienced this myself and still do on the odd occasion. If we are not aware of it, then big lessons loom on the horizon, and those lessons usually come from life in the form of a proverbial brick - sometimes the harsh lessons can be the greatest.

Sanyojana Sutta: Fetters
&quot;There are these ten fetters. Which ten? Five lower fetters &amp; five higher fetters. And which are the five lower fetters? Self-identity views, uncertainty, grasping at precepts &amp; practices, sensual desire, &amp; ill will. These are the five lower fetters. And which are the five higher fetters? Passion for form, passion for what is formless, conceit, restlessness, &amp; ignorance. These are the five higher fetters. And these are the ten fetters.&quot;

Essentially, conceit is a response evoked by fear because, through practice, we come to learn more about the nature of reality, we gain knowledge of impermanence, unsatisfactoriness, and not-self. This is enough to stir up our psychological issues around inferiority and the compensating effect of this is to bolster our identity but through the guise of spiritual-type things. We hit our fellow humans on the head with spiritualized trinkets and baubles, and poke them with incense sticks. We philosophize them into a stupefied mess of their former selves such that they take away only empty judgments.
My understanding of conceit: A sense of arrogance and superiority; a know-it-all attitude. The one-upmanship complex. In my view, conceit has an opposite which presents as an overly deflated sense of self.
I guess you'll be seeing this in your friends for some time. It is likely that they have some awareness about it, but unfortunately, it can chew people up entirely such that they cannot see themselves falling under the influence of further egoic pursuits. I don't think it would be unreasonable of you to share your observations with one of them. Maybe first bring up the fetters model as this can be a good talking point for the pursuing Buddhist, and then ask if they see any of these fetters in themselves.
Chogyam Trungpa covers this subject with great skill in his book, Cutting Through Spiritual Materialism.