Is there a search engine out there that prefers a full HTML sitemap over an XML one? On a site with thousands of articles, does it make sense to include a page that has links to every single page?
All the big search engines: Google, Yahoo, Bing, even Yandex and Baidu can read XML sitemap files. There may be some small search engines that don't use them, but all the search engines that are likely to send traffic to your site support them.
However, an XML sitemap is not sufficient, even in Google, to get all the pages on your site indexed. See The Sitemap Paradox.
Every one of your pages needs to be linked from some other page. The best way to do this is to have each of your articles link to other articles. This StackExchange site has a list of "related questions" over to the right. Much of the reason that that list is there is for search engine optimization. It helps get all the content indexed and ranked.
If all of your articles are links from other articles, there is no reason to have an HTML sitemap. If you don't have related articles, then a HTML sitemap will at least get everything indexed, even if not ranked well.
I wouldn't put thousands of links into one page. I'd instead break it up into a set of pages with no more than 500 links on any single page.