Let's not get sidetracked.
The OP has already made the decision to go with Joomla. Debating about whether to change to another CMS is pretty much beside the point...
So, back to the original question. Most CMS's these days are reasonably SEO-friendly. Each one has its quirks, but it's really not that hard to make them reasonably search friendly with just a little bit of thought and planning.
You want to make sure you have the ability to assign each page a unique HTML title tag. If you can set an HTML title tag separate from the page headline, that's even better. But at least be able to assign a unique title tag to each page. Very important.
You want the ability to create a unique meta description for each page, too. It won't help with ranking, but a well-written description has a good chance of showing up as the snippet in search results -- and it can make a difference as to whether people click through to your pages -- so you don't want it to be generic, same-on-every-page crap.
If possible, you want every page to be accessible through one URL, and one URL only. This is sometimes a problem for CMS's, because pages can be classified in more than one category and can be tagged with multiple terms. The page URL can vary depending on whether people accessed the page via one category archive or another.
Wordpress uses "permalinks" to at least partially get around this. I'm not familiar with whether Joomla has that kind of feature built in or if you need to install an extension, but either way it's a good thing to make sure you have in place. Another alternative is the rel="canonical"
element; you can use this if you have to, but the better solution is to have each page accessible via only one URL to start with.
A well-thought-out site architecture with good, descriptive navigation links (do your keyword research) will also serve you well. People often overlook the power of internal navigation links when SEO'ing a site. Having strong anchor text internal links and navigation will help put you ahead of the game.
If you have these sorts of things "baked in" to the application, you should be in pretty good shape.