At this link you can find a very good explanation, but it's only in Japanese.
Let me take out of that site the picture below and give a quick explanation. First of all we can divide all the ways to express a judgement in three groups:
This image belongs to Japan foundation: 「Copyright Japan Foundation」
Basically the main difference is the degree of dependence that the speaker has on the information. As you go from group 1 to 3, the degree of dependence on the information increases. On the other hand, if you go from 3 to 1, there is an increase in subjectivity on the judgment. That is, the speaker's subjective judgement becomes stronger than the information. So not surprisingly this is basically saying that the judgment is either objective or subjective depending on whether the judgment itself is stronger than the dependence on the information or the other way around. I realize this is probably more confusing than helpful so let's look at some concrete examples as well:
Suppose you come back home and find the house messed up (open drawers, a flower bin dipped over on the table etc). What would you say?
These are from group 1: you think thieves came into your house but you don't have enough confidence to state that clearly.
These are from group 2: your confidence that actually thieves broke into your house is somewhat getting stronger. For example you noticed that jewels and money are gone, and with this added information your imagination gets close to conviction.
Suppose you also casually look at the window and notice that the glass is broken. Then you have no doubt someone broke into your house and you would use one from group 3 such as:
The article also goes on with another interesting example which I suggest you read. If you do not understand it or feel this answer is still not clear enough, please let me know and I will expand it.
EDIT: I got carried away with the general answer and forgot to mention your specific case. Another common use of そう is when reporting not first-hand information but rather something that was heard from a friend or the news. So in the case of your plane そう is most likely used to indicate that such information is coming from some other source (as it seems to be if as you say they're likely to come from past statistics etc) rather than a direct observation. However... if this was the case the construction would be "verb (dictionary form) + そう" so it would be 混むそう. 混みそう indeed makes us think of some impression of something that "looks crowded". Where is this sentence coming from? Could it be a typo and it should actually be 混むそう instead of 混みそう? I realize now my answer might be off. Please leave a comment and if it doesn't help or it's too off I'll remove it.
EDIT 2: So, I would say it this way. Suppose who wrote the news is familiar with the information he/she is delivering (which makes sense). In this case 混みそう is not wrong and I think it is a good choice because it expresses, also according to this answer, a lower degree of certainty than ようだ. Besides, to the extent of my knowledge ようだ expresses a speaker's subjective conjecture based on information obtained through his/her sensory organs (hear, smell, touch etc). Not sure how this is related in this specific case but also it seems that そう involves a big degree of concern on the speaker's side while in the case of よう such degree is lower. See for example see this page as well. Anyway, putting all these together makes me feel 混みそう is the right choice here. About はず, I think it just doesn't work here, maybe it would sound as "it should be crowded (according to my (the writer's) subjective feeling rather than objective data).