Redirecting to the new site will not hurt SEO if your only issues are poor SEO and low PageRank. Poor SEO is just a design issue and doesn't have a negative connotation other than hurting your site's ability to have its pages rank well. Low PageRank is just due to having few links pointing to your pages. That's not a negative SEO signal.
So you should redirect your users to your new site so you don't lose the traffic you have. You also get to carry over most of the little PageRank you have to your new pages (not that PageRank really means anything anymore). It also will help anyone who clicks on a link to your old site to find the new site.
If your site has been penalized or use(s|d) black hat SEO techniques or any other negative ranking factors, then a redirect would not be a good idea as you run the risk of carrying that over to the new site. In this case, you have so little to lose from and SEO perspective that not redirecting and losing that little bit of traffic is worth it in the long run.