First it should be noted, that at the time of writing this, the XML sitemap module is not working on Drupal 8, which makes Simple XML sitemap the obvious choice for Drupal 8 installations. However, there is effort to port the XML sitemap module to D8 stable, see this queue. This comparison may be interesting for XML sitemap users moving to Drupal 8 or for users intending to wait for the port. (Do not wait, help out!) Please also be advised that gbyte made Simple XML sitemap, which makes this comparison intrinsically biased.
What sets the modules apart are their complexity, performance and feature sets.
Having been built specifically for D8, simple_sitemap has arguably a cleaner code base adhering to D8 standards i (i.e. use of OOP). In contrast, the xmlsitemap module will have a hard time adjusting to D8 technologies and guidelines, as it carries around a whole lot of legacy code going back as far as Drupal 5.
What is meant here is the impact of the module on a Drupal 8 system, how quick the sitemap generation process is and how long it takes for a visitor to fetch the sitemap.
Sitemap generation performance
Both the modules feature the batch API which allows to generate huge amounts of links without hitting any PHP limits. The sitemap generation performance differs in that it is a one step process in simple_sitemap as opposed to the two step process of the xmlsitemap module.
While the simple_sitemap's one step process is less error prone and initially generates the sitemap quicker, xmlsitemap's two steps have the advantage of tracking which entities have changed since last generation through implementing an additional database table making sure the subsequent rebuilds are quicker.
Sitemap fetching performance
When it comes to fetching the sitemap, both modules cache them: xmlsitemap creates a physical file, while simple_sitemap caches the sitemap in the database.
Both modules have the ability to set the maximum amount of links included in the sitemap and they generate multiple sitemaps along with an index if this amount is exceeded.
Consequently there should be no noticeable difference between the two modules when it comes to fetching performance.
Overall system impact
Because of its leaner code base and the fact that the code does not get invoked through hooks all to often, simple_sitemap's footprint is smaller.
Both of the modules support all core content entity types like nodes, taxonomy terms, menu links, users, etc. as well as contributed entity types (e.g. commerce products or media) out of the box. This is possible due to the great D8 entity API. Whereas xmlsitemap keeps its bundle settings on a designated page, simple_sitemap incorporates its bundle settings into bundle edit pages, which seems a bit more intuitive. Both modules allow overriding of sitemap settings on a per-entity basis.
XML Sitemap standards
Here the edge goes to simple_sitemap, as it features the newer hreflang XML standard developed by google. Adhering to Google's standards is important, as this is the search engine most of us would like to correctly understand and index our site.
Having been around since 2007, the xmlsitemap module has had lots of time to incorporate various additional functionalities which are not present in simple_sitemap yet. Automatically sending the stiemap to search engines, the ability to further customize XML output are some of these functionalities.
The new 2.x version of simple_sitemap has caught up some by implementing batch operations and drush support.
Which one is right for me?
At the moment simple_sitemap is your only option. As soon as xmlsitemap is fixed for Drupal 8, you will have to decide: simple_sitemap for a more performant codebase with the newer sitemap standard, or xmlsitemap for its bigger feature set and a smarter sitemap generation process.