There are a number of variants on how to write BEM classes, so be aware that are multiple competing standards. It started as a set of loose guidelines. Since posting this answer, Yandex has significantly overhauled their official standard (it's quite an improvement). The version of BEM I use is based heavily from an article by Nicolas Gallagher.
At this point I use "Atomic OOBEMITLESS", which is really just a way of saying that classes are modular and namespaced, selectors have low specificity, and states may be toggled with classes which allows CSS to be scaled, on top of a CSS preprocessor to make the code more concise and expressive.
All that said, I will be using the following BEM standard:
- hyphenated class names as blocks:
foo-bar
- block name followed by
__ followed by hyphenated class names for elements:
foo-bar__fizz-buzz
- block or element names followed by
-- followed by hyphenated class names for modifiers:
foo-bar--baz, foo-bar--baz__fizz-buzz, foo-bar__fizz-buzz--qux
BEM short form: block-name__element-name--modifier-name
You have three different blocks in your examples:
sidebar, which has a sidebar__nav element
content, which has a content__nav element
nav, which has nav__item and nav__link elements
The sidebar and content blocks appear to be variations on the same block, and could be represented as .region.region--sidebar and .region.region--content.
The nav block is implicit on the ul element, and you should make it explicit:
<ul class="nav"><!-- could be content__nav or sidebar__nav as well if you choose -->
<li class="nav__item"><a href="#" class="nav__link">LINK</a></li>
<li class="nav__item"><a href="#" class="nav__link">LINK</a></li>
</ul>
Once you've specified that the ul element is a nav block, it makes sense to have the nav block be modified:
<ul class="nav nav--content">
<li class="nav__item nav--content__item"><a href="#" class="nav__link nav--content__link">LINK</a></li>
<li class="nav__item nav--content__item"><a href="#" class="nav__link nav--content__link">LINK</a></li>
</ul>
Once you've set up the CSS classes, styling all nav__item elements is simply:
.nav__item {
...styles here...
}
and overriding those styles for the content nav__item elements is:
.nav--content__item {
...styles here...
}