比 comparison structures: positive adjectives?
Personally, I've never heard about this as a strict grammar rule. You can say both versions of the same sentence as:

他比我高 vs
他比我矮 
or
他比我富有 vs
他比我穷

and they would be equally correct, even though I can confirm the first ones FEEL better to me. I guess it has to do with the tendency of Chinese culture to point out positive qualities, or qualities perceived as such. As in the example, it's better to be tall than short. It's better to be rich than poor.

The negation is also performed on the positive quality. 
The same behavior can be found in western languages. It's always nicer to speak in euphemisms even if you're not making comparisons. "He's not so handsome", as opposed to "he's ugly". It's a sign of politeness. 

If you want a more philosophical-sounding analysis, you can think that it's easier to speak about the presence of a quality, instead of its absence. What you first notice about a tall person is that she's tall, and not that she's not short. 

As for your question, what are these "positive" qualities? 
Well, it all comes down to what defines a socially successful person: tall, rich, nice, handsome, smart are all good examples. 
You can apply the same intuitive principle to things and concepts, even though the boundary is more blurred here: is expensive better than cheap? 
It depends. By looking at what kind of comparisons people make, you can also get a few hints about their personality and social status.