A/B tests and multivariate tests are each suited to different sorts of experiments and websites.
When to use A/B tests
A/B tests allow to you to test two entirely different versions of a page. You might want to create an A/B test if:
You want to move things around on a page or try a different layout.
You want to alter the overall look and feel of a page.
You are able to create and publish new versions of an existing page
When to use multivariate tests
Multivariate tests let you try different combinations of content on the same page. You might want to create a multivariate test if:
You get a high amount of page traffic (more than 1,000 pageviews a week).
The layout and overall design of your page will stay the same.
You want to change specific parts of your page (such as a headline or image) simultaneously.