As mentioned, with a better rod the action, feel, and weight is usually a lot nicer than a comparable rod of lesser value. That specific action you are looking for that just clicks for you is a lot harder to find in a cheaper rod that has not had the r&d, suggestions from customer and pro staff, tweaks etc that a more expensive rod may have into it. This elusive "perfect action" especially comes into play with fly rods as the action plays a bigger part in your casting, and everyone has a different casting style.
The components are better, the cork is nicer and there is more attention to detail in the build. A lot of times there is more fishing than catching going on, so sometimes it is just nice to have something in your hand that feels and looks superior that puts a smile on your face.
Most higher prices rods are built from scratch in the US or at the very minimum the blanks are rolled else where and assembled in the US. That alone raises the price a lot from having everything done in Asia.
A really good warranty is a also big factor of the increased cost too. While a lot of cheaper rods do come with a good warranty, it will be for a year or two not lifetime, or once the rod is discontinued you are out of luck. Sage for example has a lifetime warranty, and because they roll their own blanks in house, even if you break a rod that is ten years old and discontinued 5 years ago, they will still build you a new one from scratch.
All that said, will a more expensive rod catch you more fish? No. Will a more expensive rod be more pleasurable to look at and feel and translate to a more enjoyable experience on the water? Yes. It is up to you to decide if the price difference is worth it. Also, the most expensive rod is not necessarly the best rod either.