Of the three classes of baddies: viruses, bacteria, and protozoa cysts, the last one is also the biggest in size. Pretty much all backcountry filters -- including the lighter, simpler, cheaper ones -- can block out protozoa. Filters that can also block bacteria are more intricate and bulkier and heavier. The few that can also block or treat viruses are usually bigger and heavier still.
Chemicals kind of work just the opposite. The tiniest things (viruses and then bacteria) are the easiest and quickest to kill. It is protozoa, given their size and protective shells, that are the hardest to kill.
So in a long-winded way, I guess I am just surprised that you would ditch filter for chemicals because of protozoa! That's actually where filters outshine chemicals.
Aquamira, Katadyn, and others make various models of bottle filters that will handle both bacteria and protozoa.