I know that a number of design features contribute to a superior saw. So what makes a great saw great?
The number one required thing for a hand saw is that is cuts straight. This isn't something that you can tell just from looking at it (usually - if the saw plate is bent then it clearly won't cut straight). A saw will cut straight when it's filed correctly and set evenly (to say nothing of the user's ability to cut a straight line).
Next, a great saw is made of great steel. By this, I mean a good spring steel that can hold an edge. If you've ever seen someone "pluck" a hand saw to have it make that twong noise, they're testing the springiness of the steel. Modern, boutique saws use good steel with re-file-able teeth. Big-box makers usually use induction-hardened teeth, which cannot be easily resharpened in the home shop.
The final thing that sets a great saw apart is the fit and finish. If you look at a junky big-box saw, it's all plastic, aluminum, and rubber with little thought to aesthetics and ergonomics. A properly-made hand saw is beautiful to look at and feels wonderful in the hand, even after sawing away for an hour. Great saws age very well and develop a nice patina. Cheap saws look like junk no matter how old they are.
There are of course varying degrees of greatness, even within great sawmakers. Veritas makes some excellent saws at a good price point because they are able to automate a lot of the processes that go into it. Someone like Rob Crossman, Bad Axe, or Lie-Nielsen uses processes that are more labor-intensive, thus have a higher cost. Also, you are paying for a name for some of these as well.
There are plenty of vintage/antique saws that can be made to work just as well as a new saw. Take a look at this Lumberjocks forum thread if you don't believe me.