Militarily, Rhaegar probably isn't a prodigy. But so what? I'm confident Tywin wasn't a great combatant personally. And for all Robert's skill with a hammer, he was a terrible king. By the Trident, Rhaegar was fighting a war that others had created and exacerbated (Connington, Mace Tyrell and Aerys, primarily).
Also, Rhaegar didn't "abandon" Elia, Aegon and Rhaenys. He left them in KL, which is a very defensible castle, and the Red Keep is even more so. Perhaps he might have sent them to Dragonstone, but he couldn't have reasonably predicted that Tywin would betray Aerys as he did. And in the event, Dragonstone fell too. Where else could he have sent them? Dorne? Possibly, but they wouldn't have been any safer there, Robert and Tywin would have chased them.
The point with Rhaegar is that he slightly but fatally misjudges the AA prophecy, and brings about the rebellion in pursuing it, but that he's more fondly remembered than Robert by essentially everybody.
Source:
http://asoiaf.westeros.org/index.php/topic/85629-rhaegar-overestimated-or-underestimated/