How can faith-based systems like Christianity indict or criticize other faith-based systems
Simply put no. This question seems to have an embedded assumption which dichotomizes reason and emotion. First, that division is a bit dubious given the recent discoveries in science. Second, all knowledge, relationships, and world-views are faith-based to some extent. (sorry, I don’t have time to unpack this here, people far smarter than I have done so)
There are at least 4 ways to evaluate other faith-based systems:
1) Resonate with personal experience (empirical)
2) Internal coherence (rationalistic)
3) Resonant with history (empirical)
4) Worldview results (science and empiricism)
This question suffers from:
1) a false either/or dichotomy (a logical fallacy, which fails a rationalistic evaluation)
2) failure to define or understand that reason and emotion might overlap–and be integrated. In fact, mindfulness suggests just such an integration is superior.
Phenomenology and the work of Michael Polanyi and others in the philosophy of science call into question these notions of detached “objectivity” this question assumes. (as does science itself, given cognitive biases and heuristics). Most any sociologists would question a uni-dimensional framework approach like this.
In fact, if you take a look at the most recent Star Trek, you would be wise to realize the problem at the heart of a Spockian approach to live, ethics, relationships, or reality that have been at the heart of the show since the beginning.