I have limited experience with both. Here are my 2-cents worth: There is no one best way. Each challenge may require a unique solution and that can be a combination of techniques. Both are great tools to have in your box. Fishtapes are used primarily to pull wiring through established paths, like conduit or raceways. They are almost useless in an unguided "push" scenario like in a wall cavity, but they offer greater length (25-50' or more) and strength vs fiberglass rods. The rods do give you some ability to "push" your way to a target over relatively short distances, but they are pretty much limited to straight lines unless they can follow a gentle radius along some guide like ductwork. They are insulated, so pushing through spaces that may carry live wires is not likely to be a problem with a rod. Another advantage of the rods is the variety of interchangeable tips available. In wall cavities, fishtapes are generally useless unless it's a straight drop with limited obstructions and you can reach in to find the end.
For vertical drops through insulated walls you will generally use the rods. If you have a straight run from one opening to another, this is usually fairly simple and you can join rods for a longer distance. Push the rod(s) through and use it to pull the cable(s) back. If you have to make a "bend" around a corner, or meet in the middle from two ends, you can use the metal tip on one rod to "find" a magnet on a string attached loosely to the other rod and pull that string toward you. Ultimately that string will pull the cable(s). The magnet technique helps also when you have a limited opening on both ends and the chance of hitting it is limited, like a drilled hole through a sillplate.
I don't have a lot more to offer. I'm sure others will. Good luck with your installation...!