This is from memory, so may not be completely accurate.
Bleach is not great for water treatment.
Household bleach is somewhat unstable; I don't know how long it'll remain active on trail.
It's operation is affected by pH, mineral content, temperature; city water systems have all this controlled, but you won't.
Not effective for giardia and cryptosporidium.
Worcester, Mass used to use chlorine in it's city water and had cryptosporidium in the city water. I think they switched to chlorine dioxide (like aquamira).
Bleach is effective on viruses, but in the USA viruses are less likely than bacterial problems or giardia or crypto.
From my reading, I'd say that:
Boiling is best but takes a lot of fuel; probably the best solution in midwinter.
Aquamira tablets are OK, but take a long time to kill giardia or crypto.
Better would be a good filter that removes crypto, giardia and bacteria and add bleach anyplace I was worried about viruses. Sawyer makes a good filter for bacteria; there are threads on MYOG gravity filter using the Sawyer 0.1 micron filter.
I just bought a steripen UV device and will use that, though the thought of drinking deactivated bacteria and protozoa creeps me out a bit (completely irrational).