what are the differences (and when to use) selenium-webdriver over webdriverjs?

WebDriverJS and selenium-webdriver are both JavaScript bindings for the Webdriver API.

The only difference is that selenium-webdriver is the official implementation maintained by the selenium team, whereas WebDriverJS is not. WebDriverJS is maintained by a third-party.

They do basically the same thing. The main difference is how you write your tests. selenium-webdriver is a mix of promises and callbacks - WebdriverIO only works with promises and can be used as standalone or with an internal testrunner. There is also a library called wd.js. Here is an example of how all three flavors.

selenium-webdriverjs:

driver.get('http://www.google.com');
driver.findElement(webdriver.By.id('q')).sendKeys('webdriver');
driver.findElement(webdriver.By.id('btnG')).click();

WD.js

browser
   .get("http://www.google.com")
   .elementById('q')
   .sendKeys('webdriver')
   .elementById('btnG')
   .click()

WebdriverIO:

browser
    .url('http://google.com')
    .setValue('#q','webdriver')
    .click('#btnG')

WebdriverIOs concept is to wrap all protocol commands in handy action commands but it has also almost all protocol commands implemented, so you can do the same with the standard JSONWire protocol commands.

browser
    .url('http://google.com')
    .element('#q').then(function(res) {
        return browser.elementIdValue(res.value.ELEMENT, 'webdriver');
    })
    .element('#btnG').then(function(res) {
        return browser.elementIdClick(res.value.ELEMENT);
    });