As others have pointed out, Cordelia had a choice in her involvement with the scooby gang and then with Angel. In addition, when Cordelia really became involved with the supernatural stuff, in Angel, she was much older than Buffy was when she was called as the Slayer.
Not to mention, for a while in Angel, Cordelia wasn't really involved in the killing of Demons or protecting the world... She was there for Angel. To help him. As emotional support, in addition to occasionally helping with research and tracking. She never really got into it at the level in which Buffy had to.
Buffy had to protect the world on a daily basis. It was her calling, her responsibility, from a young age and throughout her life. Cordelia could've quit any time that she wanted, she had that choice and Buffy didn't. Buffy had to make decisions that not only effected her but everyone around her. She frequently put her life at risk for people that she didn't even know... Cordelia in HS would've never put her neck on the line for anyone, much less a complete stranger. She became involved with Buffy and the gang, yes, but much less so than Willow, Xander and Giles. Given all of those things, I don't think that it's possible to say that Cordelia could've handled being a Slayer better than Buffy did. Not to mention the fact that Cordelia probably wouldn't have lasted very long. She wouldn't have had the support system that Buffy had because as much as Cordelia eventually grew as a person, she was utterly unlikeable to most of the people around her.. Buffy's friends and family is why she is still alive, even after she died a couple of times.   See 9 other replies

yeah, i see where you're coming from with the whole "if she had gone through what buffy did" thing, but honestly, i have to disagree. i really do think that cordelia would be able to keep better hold of herself, because she seems more in touch with herself than buffy does, and she doesn't seem to depend as heavily on the people around her. i think that cordelia would be able to detatch herself enough from certain situations in a way that buffy can't.   See 9 other replies