I've been using the Sawyer Squeeze for three years, but it only worked really well the first year. It takes a lot of arm strength to squeeze and needs flushed constantly now, even after cleaning the flow is very slow. I have a LifeStraw bottle like the Katadyn I haven't used yet, if it's not great in terms of flow I will probably get this Katadyn talked about, as it seems the most easy/efficient way to get water. There are also screw on filters for Nalgenes/etc (the Katadyn and LifeStraw are compatible, I think). I've used a UV water purifier which is extremely easy, while expensive, however it isn't a filter so sediment, etc, will still be in the water. Iodine tablets are always in my pack as backup but they leave a bad taste and take a while to take effect. Fine if you're overnight, not so great if you're trying to get somewhere. Never used any of the more expensive gravity filtration systems.
I *always* filter my water on every hike but not everyone does, I guess YMMV. don't know about giardia in particular on Whitney.