A quick schetch of a Maslow-ish “hierarchy of needs” for belief systems.
Is it functional? Does this way of thinking help or hinder us in our interactions with the world? Belief systems that provide better “results” (creation of technology, feelings of well-being, etc.) can be thought of as “better” than belief systems that are not as functional. There is not necessarily a strict ordering here; functionality is contextual, and what may be more functional in one setting may be less so in another. In general, we can expect belief systems that provide more functionality on net to gradually become dominant within the noosphere.
Is it internal consistent? Belief systems that are internally consistent can be thought of as “better” than those that are compartmentalized and non-aligned, in that they will be easier to teach to subsequent generations. They will also be more likely to fulfill higher levels of belief system “need”. In general, an internally consistent belief system will also be well-defined.
Is it extensible? Can the belief system be extended to “think more interesting thoughts”? An system of belief that allows for an infinite number of thoughts to be explored will be more interesting/pleasurable to think in than one which is finite. The most best understood extensible belief system is probably mathematics, courtesy of Gödel's incompleteness theorems. This is one reason why formal math can be so much fun.
Does it allow us to think interesting things? This is more subjective, but belief systems that allow for more complex, interesting ideas will be more pleasurable/fun than belief systems that restrict our ideas. Belief systems that tie together more realms of experience (“larger infinities”) will be more interesting/pleasurable to think in than more limited belief systems. Formal mathematics has only tenuous direct connection to human experience, which is why most people don't find it very interesting.
Does it allow us to think meaningful things? This is the aesthetic level… Does the belief system appeal to our sense of truth, beauty, or ethics? I propose that meaningful thoughts are always interesting thoughts, but that not every interesting thought is meaningful.
Note that what is “interesting” and “meaningful” may very well change with time… What seemed profound to our ancestors often will appear to be quaint to later generations. Belief systems that cannot continually allow for the borders of “interesting” and “meaningful” to be expanded will lose their value over time.