Vendor-neutral vs. vendor-specific security training

Which security certification training is better -- vendor neutral or specific?

That depends on what kind of work you want to do and what kind of environment you're working in. In a single vendor(homogenous)environment, vendor-specific certifications are most germane and therefore most useful. If you work as a consultant with multiple clients, or you work in an environment with solutions from multiple vendors (pretty typical nowadays), vendor-neutral certifications will be most germane, and therefore most useful as well.