Not sure how WP Engine works, but you setup a permanent 301 redirect, which Google will pass link juice through, meaning any old value to the pages will flow through to the new version. Personally, I do this in my web server to pick one version and stick with it, but there are other places to set your site up to “pick a URL”.
The WP thing itself likely has a lot to do with the URL you were on when initializing the blog. If you are comfortable and WP Engine allows it, you may be able to tweak WP to use your preferred subdomain.
Also use the canonical meta tag so each page identifies the correct version of itself.
WWW or not makes no difference by itself, consistency is key. Google does not say to itself “this one has it, so its better”. But they do see 2 pages that have two different sets of ‘values’.
The 301 will pass along any page value coming in from external links to old URLs. The canonical tag will help G understand what you “meant” to do and that the copies of a page are not actual copies, just that there is more than 1 URL route to the only version of content that matters.