This is going to be a short article, because there is next to no difference in performance between casting a modern, graphite 2-piece or a 4-piece fly rod. In the hand, they feel identical. Either, will cast just as far and with comparable accuracy. Budget is also not a consideration, even cheap 4-piece rods have well designed ferrules and minimal flat spots.
The main difference between 2- and 4-piece fly rods is in portability, 4 section fly rods simply take up less space and pack away smaller. They are much easier to store and are much more practical to travel with. Perfect for hiding away in the trunk of a small car.
I also want to note, that warranty repairs are usually cheaper on four piece rods than two piece. This is simply because each section is smaller.
Are there any advantages to a 2-piece rod?
A 2-piece rod is certainty a lot more transportable than a single piece rod, but these are next to non existent these days.
They are ever so slightly faster to assemble. Only two pieces to join together not four, this also makes them slightly easier to assemble in the correct alignment. Perfectly straight.
2 piece rods, might be ever so slightly more durable than a four piece, because ferrules. That is the joining portion are prone to damage. They are also prone to getting stuck together. This is not a major issue, and personally I do not consider it when buying rods?
I also suppose, it is more difficult to lose a section of a two-piece rod. Simply because there is only two sections. Over the years, I have lost a couple of tip sections of four-piece rods, usually when they snag on vegetation when pushing through thickets when targeting trout that live in overgrown streams.
Some people find 2-piece fly rods are easy to split in half while fully this, and store with both sections end to end. Will, it is also possible to separate a 4-piece in half and transport them in a similar way. This is exactly what I do when driving between fishing spots, I split my 2-piece at the middle ferrule. This makes getting back on the water very fast.
Conclusion
Will, this is just about everything regarding the difference between modern, graphite two and four piece fly rods.
Now, what I said only applies to more modern rods, Say rods designed in the previous 25 years and from graphite. If you are looking at vintage or fiberglass rods, then a 2-piece rod might offer better performance.