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Does the blog platform matter in ranking on Google SERPs?
Nope! Not one iota. The platform a blog is using is just a platform, nothing else. It's all about the content that sits upon that platform, the way that content is and what the off-page SEO of it is. The platform it's using will not even be considered by Google. Firstly because not all sites show what platform they are using and some can be different platforms but still use the exact same content. Example; HTML/PHP.
What content management system or what blogging platform you are using does not matter in Google SERP. What actually matters is design of your site, contents on your site and backlinks on your site.
In order to get high SERP, you site should have easy to navigate design. Your contents must be unique and original, your site should be backlinked to high authority sites and your site and contents must be optimized for search engines.
What you really need to have a look at is the content that is on the blog. I mean that in as much as we try to find better ways that we can rank on Google, using content has been the best bet of it.