Sometimes, not only in English but in all languages, we want to emphasize certain situations. And then the language itself gives us devices that aren't always common, but we use them anyways, based on known and meaningful expressions.
I am very hungry
We can depict that the subject has surpassed the status of just "hungry" for they must have stayed a long time without eating. This is a known meaningful expression.
Murder is very illegal
From this, even if it doesn't make much sense in the binary nature of the word "legal", we can depict that "murder" is a crime that, morally or ethically, has surpassed the status of "illegal".
We can state that by looking at another not-so-serious crime:
Parking on the sidewalk is illegal
Yeah, we all know it is illegal and wrong. But it is a petty crime compared to murder. In some countries murder is penalized with life imprisonment, even with death penalty, while parking on the sidewalk gives you a fine and, in the worst of the cases, your car is towed.
We can still say that "Murder is illegal", of course it is, but in the sentence, the "very illegal" was made to emphasize.
Best Answer
As you pointed out, the main (and probably the most striking) difference between 'might be' and 'would be' is in the degree of certainty.
'would' is a modal verbs, and is the past tense of 'will'. By using 'will', the certainty of the event happening is most likely. The speaker thinks that taking a rest after work is a good thing to do, and he is almost completely certain that this is advisable.
Much like 'would', 'might' is also a modal verb, and is the past tense of 'may'. In terms of certainty, 'might' or 'may' has a lesser degree of certainty, when compared to 'would' or 'will'. The speaker suggests that resting is a good option, after work, and he is certain that this is true, with a hint of probability of the statement's validity.
Other than that, I don't see any striking differences between the two.
A few good reads:
http://www.differencebetween.net/language/words-language/difference-between-would-and-might/
http://www.grammar-quizzes.com/modal1.html
http://www.grammar-quizzes.com/modal1.html