I hate to start with this answer, but it is so commonly true ----

It depends on the situation!

I have a type of most of the common tools, and use them all in different situations. Part of the situation is the threat of various organisms in a particular area. Where crypto is present, some of the chemical products (iodine and chlorine) don't work at all and the others are very slow. Where the viruses are present, most filters won't do the trick and need chemical treatment after filtering. Temperature is a problem for all of them except boiling, but different. For the chemical techniques, the time is lengthened considerably (which is already a problem with these techniques). For filters, damage to the filter from freezing has to be delt with. The SteriPen is battery operated and must be kept warm to work.

Katadyn Pocket Filter - great for a small group on the move where water is not universal (not under you - see SteriPen). My "universal" tool. It cleans most water (viruses are a problem, but not serious in most of North America). Sweetwater or other chlorine based chemicals will solve that problem. The water is ready to use immediately.

MicroPur Tablets - The tool for psk use, OK for short trips. Small, light and kills everything. Water not available for some time (up to 4 hours if crypto is a problem) so you have to carry several containers so that you have some available all the time.

SteriPen - Super for canoeing or other times where water is available all the time (especially if it is moderately clear). More of a problem (pre filtering) if the water is cloudy. Requires care to prevent cross contamination (especially if you use their immersion technique which is not a good idea imho). Batteries which some consider a problem and some do not. Water is available immediately. Slow if you need lots of water at one time.

MSR MIOX - Great for large groups (works well in bladders and other large containers) and stationary situations (I use mine a lot when working out of a base camp, fill a bladder in the morning and it is ready when I return - fill it in the evening and it is ready in the morning). Like the tablets, it is not the best for traveling because of the time potentially required. This requires lots of planning and containers (or multiple large containers).

Boiling - The most commonly used, why purify water if you are using it for tea or to reconstitute foods? Once it has boiled it is OK in most parts of the world. If you have an open fire it is a great technique for large volumes of water, but requires lots of capacity or stopping for fires during the day. Seldom do I use this by itself on a trip, but every trip I use it some.

I like and use all these tools. If I had to pick one it would be my Pocket Filter with the backup of SweetWater for areas with a virus problem.

Respectfully,

Jerry