It is important to understand that security assessment methods can use either black-box or white-box methods, and can be based upon either automated or manual methods. All 4 combinations are possible (e.g., automated black-box pentesting tools; manual black-box pentesting; automated source code scanners; manual source code review). Also, it is important to understand the difference between a security architecture review (looking for architectural/design issues) and a code assessment (looking for implementation bugs); usually, black-box and automated methods are mostly focused on the latter. I'm going to assume you are focused on a code assessment, looking for implementation bugs.
With that background, here's a suggested checklist to help you decide which method to use:
Do you have source code? If no, use black-box testing. White-box methods require source code.
Have you ever done any kind of security testing, pen testing, security code audit, or other security assessment before? If no, use black-box testing. It is cheaper. Start small and work your way up.
Are you just in it to comply with a mandate, or are you trying to protect your own systems? If this is just about compliance, choose whatever the cheapest answer that will get you to the checkbox (typically black-box testing).
If you've made it to here, you'll need to do a cost-benefit analysis. I would suggest starting with the cheapest methods, use them to improve your security software development lifecycle. Then start by gradually easing into white-box and manual methods, and evaluate the value to your business.
Generally speaking, black-box testing is cheaper than white-box methods, but black-box testing finds fewer bugs. Generally speaking, automated tools are cheaper than manual methods, they scale a lot better to large codebases, and they are better-suited to periodic scans/reviews, but automated tools may find fewer bugs than manual methods.
See also White-box vs. Black-box, Do blackbox penetration tests make sense if a whitebox audit would be possible as well?, Expected cost and time frame for black box pen testing?, How much does a security audit cost?. Don't forget to try using search before posting a new question -- there's lots of good stuff already on this site!