Chlorine has no affect on Crypto and at most a moderate affect on Giardia according to the CDC. GCNP and health organizations recommend pairing chlorine with filtration first.
Here is why:
Filtration: the vast majority of filters we use only go down to .3 micron which is only moderately successful at eliminating bacteria but highly successful at elimating protozoas (crypto and giardia) and has no affect on viruses (less common of issue stateside if pulling from side streams)
Chlorine is highly successful at killing bacteria and viruses but limited to no impact on protozoans.
Hence the combo if you are worried about water contamination.
Now.....Aqua Mira, aka Chlorine Dioxide, is highly successful at killing bacteria, viruses and giardia. It is moderately successful at killing Crypto (that success goes up if you wait upwards of 4 hours).
CDC - A Guide to Drinking Water Treatment and Sanitation for Backcountry and Travel Use - Camping, Hiking, Travel - Drinking Water - Healthy Water
The CDC is the most reliable source for testing these issues at this point. They are at least consistent in their methodology and reporting.
Your tools will depend on your concerns:
1) Filter/chemical: Worried about all contagions
2) Filter alone: Worried only about protozoans
3) Chlorine alone: only worried about viruses and bacteria
4) Aqua Mira alone: worried about bacteria, viruses and/or giardia OR willing to wait 4 hours (colder water actually decreases efficacy of most chemicals) to kill crypto
5) Nothing: not worried about potential contagions