Earlier quoted context omitted.
In a way, yes, they do. Chrome pushes out a dozen or more fixes for remotely exploitable vulnerabilities every 2 weeks.
No they don't. Chrome is designed from the ground up for security. It has the same number of bugs as other software of it's size but the type of bugs are much less severe. Compare FF, Safari, IE, Chrome. Same number of bugs per yet but Chrome has 10x less code execution bugs (ie, 10x less likely for your machine to be owned by unknown bugs) http://i.imgur.com/rVgu7Fs.png
Flash runs in a low-priv environment is nearly every major browser, includes application-specific exploit mitigations, and it silently auto-updates, just like Chrome. It's all a matter of the Flash install base: it's in 90%+ of browsers and it's running the same-ish codebase in all of them, making it a relatively stable platform to develop exploits for. That's it! It's more a factor of market share and not "security."
Every document reader, HTML renderer, JavaScript engine, browser, media player, etc that you use is the same -- a house of cards built on poor memory management :-/.