By default? It can break a lot things that people expect to work and can make browsing the web slightly more annoying (harder recapcthas etc). You can enable first-party site isolation in your Firefox preferences which will effectively provider a container for each site (as far as I understand). But it's pretty annoying at times.
In terms of cookies that's effectively the same yes.
To deal with the annoying breaks, assuming the fix you want is 'just make it work', there's at least one add-on available that just gives you a toolbar button to toggle it on or off, a fish bowl that glows red as a warning when off.
