For almost all brands, it's not an either/or choice. Instead, when adapting your brand to a new platform, try to understand the platform's look and feel and adapt your brand's look and feel to it.
Luckily, the things that matter most in branding (e.g. logos, color scheme, graphics, and visual layout) tend to be things that platforms give developers lots of latitude to define. Don't feel you have to compromise on those things. But when designing buttons, navigation, and other lower-level UX elements that platforms tend to specify, try to align with the platform standards.
As the other posters mention, in the rare case that platform and brand conflict, go with the platform. Otherwise you end up with apps like ITunes on Windows and other platform-hostile apps which confuse users. If users don't like using your software, it won't help your brand!
There are some (very rare) cases where breaking with platform conventions are OK. If you do this, just make sure you're doing it in a smart way, where "smart" means it won't get your app booted from your platform's app store and you don't do it any more than is critical for your brand. For example, on Android almost all apps use sans-serif fonts for readable text. But the New York Times's serif font is so much a part of its brand that its apps will always use a serif font, even if that results in less-readable text. But even Times apps limit serif fonts to news article content. Other text (on buttons, headings, etc.) is the platform default.