I have a few clients with their own accounts on DH and my own account as well, all with Wordpress One-Click installs.
For some reason it seems they're all using latin1_swedish_ci collation while the mySQL connection collation is utf8_unicode_ci.
For two different accounts, both using PHP5, mySQL and WP installs, on the server tethys I am getting the 'mbstring PHP extension was not found' error and on the server kenobi I am not.
Looking at runtime info they seem to perform similarly, tethys showing some more sluggish performance. I have only "in passing" experience with mySQL though and don't know where to look. For my part, my site with db on tethys was performing extremely poorly - I submitted a support ticket. I've found that checking all the suggested 'tips' in the support section for your ticket and reporting the results in your ticket shows that you checked obvious stuff and seems (in my experience) to get better response.
In fact, in the time it took me to write this the site's response has improved greatly. Someone kicked that server back into shape or maybe it was some errant process that concluded/fixed itself. The error message in phpMyAdmin is still there but my site works so I'm not going to try to fix what's not broken on my side. That's server config stuff and should be handled by DH.