The honest answer
Neither plugin makes a site rank by itself. Both give you the same basic controls: a field for the title tag, a field for the meta description, an XML sitemap and schema output. Google reads the result on the page. It does not care which plugin wrote it.
So the choice comes down to two things. The first is what you need without paying. If you expect to change addresses and need a redirect manager, Rank Math includes one in the free version. Yoast SEO keeps it for the paid Premium version. The second is how many settings you want to see. Yoast SEO is known for a guided, simple setup. Rank Math offers more options and modules, which some people find busier.
Whichever you pick, use only one. Two SEO plugins on the same site can conflict and output the same tags twice.
The checks in both plugins are a guide, not a goal. A passed check does not mean the page will rank. Spend the time on the words instead. Start with how to write title tags that get clicked, and test a title in the title length checker before you save it. Then run the page through the free audit.
Features and plans change, so check each product's own site before you decide. For the cost of the paid versions, see the current pricing on each site.