They're both amazing frames that are great for both general purpose and nuking. Gloomy Saryn and Explosive Legerdemain are two of my favorite builds in Warframe.
Personally, I'd say Saryn is my general purpose nuke warframe. Any weapon, just about any content, I feel extremely confident she can handle it comfortably. Mirage, otoh, is my go-to Warframe for being stupidly overpowered at a particular thing, like Explosive Legerdemain for SO, Disco ESO, or buffing Exodia Contagion to extremes.
Gloomy Saryn. Great for clearing the trash, slowing disruptors to a crawl, and high survival.