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These word pairs both seem to mean "Convenient/Inconvenient". But what is the
difference between them and usage cases?

From looking at their kanji and a few example sentences, this is what I've
come up with. Is this correct?

  * 便利/不便: A physical object is convenient. e.g., "This tool is convenient"
  * 都合がいい/悪い: A situation is convenient. e.g., "That day is convenient"
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2014-06-11T14:23:50.553
17373
2014-06-11T14:41:33.910
1497
question
usage nuances
Difference between 便利/不便 and 都合がいい/悪い
都合 means more like circumstances or condition. 都合がいい would literally translate
to the circumstances are favorable (on a particular day), which makes the
meaning of "that day is convenient (favorable) for me".

便利 (as suggested by its kanjis, 便 - convenience; and 利 - profit, benefit)
means advantageous/profitable convenience, i.e. useful or handy. A situation
will be favorable and an object would be convenient.

So looking at your examples, they seem correct.
CC BY-SA 3.0
2014-06-11T14:35:42.540
17374
2014-06-11T14:41:33.910
2014-06-11T14:41:33.910
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4507
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answer