Which one of these is a better solution?
- Submitting sitemaps via a plugin like Yoast or Google Sitemaps OR
- Manually creating an xml file and submitting that to the webmaster tools?
In terms of index, it does not matter. Both will index your content in same way. It's just XML file, Google doesn't favor one over others. Google also treat XML sitemap,atom,text and rss file in same way. Also sitemap file just help you to index content, it doesn't have any relation with ranking as well.
So the difference is, If you create XML file manually, then it will take your some of time, but by doing that wordpress does not need to create automatically, so it will save some of your server resource, but again it will help to save only 0.1% resource or may be even lesser.
As @Goyllo has already pointed out, there is no difference SEO-wise between auto and manually creating/submitting the sitemap (but since you've not tagged your question
seo - maybe that isn't your question anyway?).
However, "manually" creating and submitting the XML sitemap is going to be laboriously time-consuming and prone to error. Once the site gets beyond a certain size then manually creating the sitemap will quickly become "impossible".
Sitemap creation and submission should be automated. (So that would be option#1.)
Any additional server-overhead with sitemap generation should be insignificant in terms of the day-today running of your site. (That is, assuming your "automated" sitemap generation doesn't involve a bot literally crawling your site - that could be "expensive" and possibly a waste of time anyway.)