One big downside to Magento for me is extension updates. I know they tried to fix it with Marketplace and Connect but it’s too easy for people to install extensions from lots of different places, using many different methods. This then makes it difficult to keep on top of extension updates. Tools like Magerun with Hypernode's add-on help but they aren’t 100% reliable so there’s still work to do.
This is something that WordPress does very well – it makes it really clear that you have out-of-date core software or plugins and gives you clear ways to update them.
Connect was meant to do this in Magento but in my experience developers bypass Connect because it didn’t always work very well and would often result in half-installed extensions and, of course, as developers there's always that urge to be "clever" and want to do things via the command line so you end up with a fragmented install and update process.
I believe that for software to be kept up-to-date it needs to be painless. We've all been there when you sit down to start work for the day and your laptop starts updating the operating system which then results in an hour of lost work or, if we can, we cancel the update and leave it for a while. If it's not easy then it won't get done, it's that simple. WordPress updates are easy, Magento updates are difficult so they don't get done.
I've not worked with Magento 2 much yet as all of my clients are on legacy M1 stores for the time being so I'm not sure how much this has improved. Feel free to comment with your experiences.