It's mostly a judgement call.

I THINK you might be having trouble because you're looking at the molecules more as parts rather than the molecules as a whole. If you look too intensely at either one, you'll come to the conclusion that both are polar because they both contain polar components (N and O). However, you have to consider the overall structure when determining polarity.

Consider CCl4. It's a C surrounded by 4 Cl (extremely electronegative element). Each C-Cl bond is extremely polar, however, the overall tetrahedral arrangement results in the cancelling of dipoles making the molecule non-polar overall.

Keeping this in mind, in the case of molecule 1 you've got a ton of non-polar carbon rings with polar N and O sprinkled throughout. But take a look at the overall structure of this molecule. It's overall structure resembles a rhombus, and it is almost perfectly symmetrical if you cut it straight down the middle. It's also a pretty large molecule, composed primarily of non-polar components. Remember, polarity is the result of a kind of tug-of-war with electrons. When one side pulls the electrons harder (electronegative side), polarity results. Those large hydrocarbon rings are like a group of body builders from your local gym and the N's and O's are like single professional body builders. The pros are stronger individually, but they can't quite overcome a whole group of amateur body builders in tug-of-war.

In the case of molecule 2 you've got a pretty small molecule resembling something like a triangle. The molecule is not THAT symmetrical and there are polar groups (N's and O's) at 3 significant locations (each point of the almost-triangle). This tug-of-war match is much more predictable. You've got the same pros as you had in molecule 1, and a whole lot less of the amateurs. The pros are gonna win, no questions asked.

I guess the takeaway here is look at the big picture. Consider the size, shape/symmetry, and amounts of non-polar + polar components (relative to each other) within a molecule when considering overall polarity.