If you are in camp and you have large pots and ample fuel supply to boil water with, then I would go that route.
But, if you are out on the trail and traveling light, iodine makes the most sense, and is the most time efficient. Just get some of the tablets, that come with neutralizer. Two tablets per quart for something like half an hour, then throw in a neutralizer tablet and the taste really improves!
Even if you use a filter, the filter is going to have to contain iodine if you are going to get everything...so why not just use iodine to start with???