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As far as I know both words could be used to describe
usefulness/handiness/convenience of something.

What are the main differences between them? In particular, what are the use
patterns for these words? What would be the example sentences that demonstrate
the word usage.

Are they form a formal/colloquial pair or they behave like [大事 and
大切](https://japanese.stackexchange.com/questions/11262/what-is-the-difference-
between-%E5%A4%A7%E4%BA%8B-and-%E5%A4%A7%E5%88%87)?
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2013-06-26T09:52:23.350
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question
nuances word-choice
What is the difference between 有用(yuuyou) and 便利(benri)?
The difference is pretty clear cut and I think they map pretty closely to the
English usage of "useful" and "convenient," respectively. This is one that the
dictionary will illuminate for us, so if I may...

[有用](http://www.weblio.jp/content/%E6%9C%89%E7%94%A8):

> 役に立つ・こと（さま）。  
>  ⇔無用  
>  「国家―の人材」「―な品物」「社会に―な人材」

If you look purely at the kanji you can get the idea: something that has use.
The definition for it is just an alternate way of saying "useful," or 役に立つ.
The examples from the dictionary can give you some idea, but searching alc
will show you with a lot more examples that this has the general meaning of
_being of use_.

Now for the other contender:

[便利](http://www.weblio.jp/content/%E4%BE%BF%E5%88%A9):

> 都合のよいこと。役に立って具合のよいこと。また、そのさま。  
>  ⇔不便  
>  「通勤に―な土地」「―な道具」「この辺は何かと―がよい」

It means "convenient," plain and simple. It is similar to 有用, yes, and indeed
both definitions contain the phrase 役に立つ, but 便利 expands on that a little bit
to be something that improves conditions in some way rather than just being a
thing that can be used. To clarify a little more on the difference, something
that is 有用 is something that can be utilized to achieve some good or some
goal, but something that is 便利 is inherently beneficial in some way in making
some situation better.

For example, you could say 有用な人, or someone we would refer to as a "valuable
asset" to a team or whatever, but we would not call this person convenient in
the same context.
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answer