The number of computers you use is not really relevant to which one is more useful. Sure, a NAS unit serving multiple computers would be far better than an external disk, due simply to the fact that the files are made available to everyone at the same time, but that should not be the defining factor.
The NAS will be more expensive than an external, period. When you build a NAS, you are buying HDDs to put into an empty system, and you are buying the empty system, which consists either of computer parts or a prebuilt NAS unit. Most prebuilt NAS units are not worth it for the price, so I don't even consider them. However, when you build a NAS, what you are paying for is more advanced handling of your data and more reliability. By setting up a NAS unit, you would typically also build a software layer that combines your disks together, so you see a single disk (my 6 disk array shows up as a single 13.7TB disk). You would also typically set up a RAID volume as this software layer, which allows your data to survive if one or more disks fail in your collection of disks (depends on which RAID level you pick). When you have a bunch of externals, if you lose a disk you will lose all the data on that disk. Note this does not have to be done in software - there exist hardware to do the same thing, and many Intel-based motherboards have built-in RAID capability. If you have a board without onboard RAID, a good RAID card costs hundreds, while a simple RAID card can cost under $50.
So, in the end, a NAS and an external HDD perform the same tasks but the extra benefits of the NAS kind of put it into a different category.
I mentioned Drobo in my last post but it doesn't look like you looked it up. You really should check it out.