The question depends on many variables, including person preference.
- Storing water is good, but takes up lots of space and needs to be rotated. With at least a gallon per Peron, per day. You are looking at 12 gallons minimum for 3 days. (only for cooking and drinking, no showers!) You also need to add chlorine or other things to keep the water good during storage. Also there is a risk of leakage during storage.

- Waterpurification equipment is much easier to store and you don’t need a lot of time to maintain it. It does require a lot of effort to use and you need to transport the water from a source to your home. (really no fun to drag 4 gallons of water and pump it through the filer/purifier each day). Keep extra containers handy. (make sure the purifier will work without electric power). The filter quality can be a issue. Normal filters will not remove chemicals or petrochemical products. Some have carbon element to absorb the chemicals, but they are ineffective for petrochemical products.

In general I would suggest both.