Disagree with Charles that Wordpress is 'much better' and that you'll find more design options, mostly because both are not true. Joomla is good for some things while Wordpress is good for others. Design wise, they're equal and don't let anyone tell you different. Just look at the theme providers for both.
However, Wordpress is easier to use. My 9 year old son has set up a Wordpress site and he liked it, but went back to Blogger. As Wordpress is easier, that also means Joomla is more complicated but at the exact same time, Drupal is even more complicated and Drupal beats both overall (although probably not for SEO but that mostly comes down to the extensions you can install for Wordpress and Joomla).
And if you're using an old version of Joomla, I'd guess 1.0 or 1.5, then the easiest thing for you to do would be to stick with Joomla but don't just migrate, first there are things to consider.
First, juice doesn't 'just' go to the domain, it goes throughout your site and each page will have some, so if you're moving platform or changing URL structure make sure and this is the most important part, that Google knows.
You can do this in a number of ways (there are extensions on the Joomle Extensions Directory to help) but the safest way would be to add some 301 redirects into your .htaccess file of your new site so when Google looks for the the URL and it ends up somewhere else, after following the redirect and seeing that it's a 301 (permanent) and accepts the new link as the right one, your juice follows with it.
There are also tools at Google Webmaster to help you know if anything is going wrong.
But it's also worth looking into where your juice is coming from and where it's going on your site. If the vast majority of it is going to your homepage then it might not be so critical on what platform you use (although I'd stick with Joomla), but just remember to do the 301 redirects so Google knows where the new pages are. And also go responsive (Google likes responsive design) and make sure your site is as fast as possible, as Google likes speed too.
Good luck ..