Most of the times client just say they want to use the CMS but after asking which CMS they prefer they say whichever is better and has more functions.
Both of the CMS platforms have there advantages and disadvantages but for the basic websites both of the platforms are good. When designing complex websites one platform may have more advantage than other but again its subjective and changes from requirement to requirement.
The link above classifies which one is better than other when compared cosmetically or aesthetically. Functionality wise one is better than other based on specific requirements.
Static websites are of no use nowadays as they cannot be kept updated so use of any of this cms platform is the need of web design today. Any web developer keeps this platforms in mind when designing any kind of websites.
I have personally used both the platforms but problem with WordPress website I have seen is they are very easy to hack. They give a back door entry to hackers so they can go inside and change all the themes, contents, username and passwords. If any plugins get updates or theme get updated we have to upgrade them or else they get hacked by hackers.
Though if proper plugins to protect the website is used this problem can be avoided. If used properly this platform can do wonders for your business.
In Joomla website I have seen its little bit hard for the clients to Understand. We have created educational videos for clients explaining how that problem can be solved but they always still face the problem understanding how to operate the admin panel of Joomla.
I hope above article will help you to decide which platform is better for your website and business.