i sometimes use a false bottom and a filter. other times i just dump the whole thing in the fermenter.
both work equally well in creating beer. one could argue that you get cleaner, clearer beers when you strain/filter/whatever, but it's not necessary to create fantastic brews.
time, finings, filter, etc. can always clear a beer long after fermentation is finished, too.
i think the #1 thing that filtering/straining does is not to clear the beer, but just to keep more crap out of the fermenter.