For a given cross section, the rod is far stronger than the same cross section of wire. Designers realize this and use a smaller section of rod to perform the duties of wire, with the reduction in weight aloft and also the reduction of wind resistance.
Early on, the caveats were: "Sure its lighter and smaller, but will it last?" In general, rod lasts longer than wire, but with some very important caveats.
First is cost, it is substanially more expensive than wire.
Second is maintenance, a wire can handle some abrasion and kinks and just keep on working. A kink or abrasion on rod calls for immediate replacement, particularly an abrasion or "dent" in the rod.
Third, you need to periodically inspect the rod ends or "heads" as they are called. This is the main area for fatigue and failure of rods. Periodic inspection and possibly "Re-Heading" the rod will extend it''s life.
Fourth, the yard has to take care that the rod is not damaged during stepping/unstepping the mast. I had my backstay run over by a forklift, seriously gouging the rod and forcing me to replace it. Because no one at the marina witnessed the incedent, the yard took no responsibility, ouch!
Finally, for extended world-wide cruising, you should probably concider wire only. If you have a failure or need repairs in some remote portion of the world, everybody handles wire, but rods require specialized tools that may not be available in a pinch.
For racing, rods are the only way to go. For cruising the civilized world, rods make some sense. For out in the fringes, go with wire.