No. The only dofferences in the two plans are in the disk space, bandwidth, nymber of email accounts, etc as described in the plan comparison page from the main Dreamhost site. They are both “shared servers” and do not differ in CPU usage/limitations or MySQL capabilities.
As you didn’t describe what CMS you are using, and we don’t know what degree of interactivity your visitors have on the site, it is impossible to tell how well your site will perform on a shared server. CMS systems, and the modules, plug-ins, etc. that often operate within them, vary greatly in efficiency of coding (which affects CPU usage) and the efficiency of MySQL queries (which affects not only CPU usage, but also impacts the overall load on the shared MySQL servers).
If it were me, I’d be looking to parlay those visitors and page views into enough revenue to host on a dedicated server. That said, Dreamhost has a 97 day money back guarantee (read the Terms and Conditions carefully, and pay with a charge card!), so it couldn’t hurt to give it a try.