The next smallest particulates in the water are viruses. This is where filters drop out of the race. Some examples of viruses are Hepatitis A, Polio, and the Norwalk Virus. They can be killed by purification, chemical disinfecting, and boiling. If you plan to do a lot of international traveling where you need to treat water before drinking you should get a water purifier.
Viruses are more common outside the United States.
There are other things to consider that should be investigated at the time of purchase. One is cost, of course. The prices for both filters and purifiers span from dollars to hundreds of dollars. You can only strain so many pots of noodles before your colander is crammed full of noodles. Similarly, filters clog and need to be replaced.