Using PHPUnit with Selenium, how can I test that an element contains exactly something?

You can pass in any Xpath to target the desired element.

$this->assertElementContainsText(
    "//p[@id='foo']/a[@href='http://www.example.com/']",
    'bar'
);

You can add the following to your base class to allow testing for exact matches on the contents.

/**
 * Asserts that an element contains exactly a given string.
 *
 * @param  string $locator
 * @param  string $text
 * @param  string $message
 */
public function assertElementTextEquals($locator, $text, $message = '')
{
    $this->assertEquals($text, $this->getText($locator), $message);
}