Boiling in a pressure cooker will benefit several ways. The temperature will be higher, the pressure greater, boiling time is reduced, and less water is lost in the boiling process..
Like donutsrule said, boiling does not remove anything from water. It will denature proteins, many but not all permanently. But it will not remove any chemicals except low pressure volatile organics. In other words, it will drive off alcohols and esthers and some other stuff, but it also drives off some of the water, which brings us to the down side:
Boiling makes water dirtier. The water may indeed become sterile, but after boiling off 5 to 30% of the water, the concentration of sediments, dirt, heavy organics, minerals like lead and uranium, and many poisons, if present to begin with, will be at higher concentrations after the boiling process. Water that had pollutants below EPA concentrations may now have them above the magic line. The bugs may be dead, but any poisons produced or carried that are not deactivated by heat, as in the basic food poisoning bug, will just increase in concentration.
I remember reading about a group of people stranded on an island in sight of a major US city for a couple of days. Saltwater all around. They were burning 3 bon fires continuously to signal for help. They had no potable water. They were sopping dew off of the grasses. Seems to me that all they needed was tubing and a "lid" with a hole in it to distill the seawater in any cup or pot. Efficiency was not an issue, the fuel was burning anyway, and lots of cool seawater to cool the tubing......