Context is pretty important for this one.
For general websites I have always considered top navigation as primary and sidebar menus as secondary navigation. The advantage to sidebars here is where there is lots of information and having the preview of other sub-menu items highlighted can expedite users finding what they're looking for.
E-commerce and catalogue type sites are very commonly using top menu for navigation/categories and the sidebars for filtering. There advantage there is just narrowing down results as you're commonly on a second page at this point so leaving the main menu alone is just keeping things standard.
Web systems with more of a dashboard feel fairly commonly user sidebar menus. I'm not sure if this is advantageous or just common practice for web. I'm working with lots of touchscreen dashboard types interfaces these days so there are huge advantages here just with my users environment.
For a Responsive Web Design I don't think I would touch sidebar navigation unless I had a strong Use Case pointing me to do so.