Joomla now has a plugin WordPress for Joomla. I haven't used it personally, but the ratings are pretty good. I have installed many Joomla sites but now I use WordPress for a majority of the sites I install.
I also use a Joomla site with a WordPress subdirectory. It works ok, but even with good links back and forth, it can still be a little awkward for your user.
Plus, trying to get the templates and design to be consistent is a bit of a problem.
If you are not in a critical hurry, I might try the Joomla WordPress plugin to see if it integrates the design well. Also, if you have membership or other user login, you might need to consider the problem of having dual logins, a royal pain!!!
Think through carefully what you are planning to do with both parts of your website carefully before making the transition.
I'll be happy to follow up the conversation if you need more info.