I tried both when I was a beginner, more or less, and both were such a hassle for me at the time that I eventually settled for a Wordpress-hosted Wordpress. I have a lot of experience with WP, relatively little with Joomla, so I couldn't really make a fair comparison between the two, but that single vote up there for "Other" is me...
I have since tried out and used just about every single set of blog scripts in existence, and what I've settled on personally is what I've been able to hack together myself out of various code snippets found via Google and some funky one-file script I found on a site that had maybe three words total in English and which was coded, if I'm not mistaken, in 2002. I used to have to tell it to ignore errors, but have since done everything possible to update the deprecated code while keeping it functional. Yes, I finally decided to be a responsible coder.
Maybe it's just me, maybe I'm weird, but it just feels good. You know? It's got a fairly light footprint for something which uses no remote database (dbs are my kryptonite), being as simple as possible means I can change things easily and make it do pretty much whatever I want, and at least two of the world's highest-traffic websites use their own modified versions of the same script, albeit for different purposes.
I'm not in any way trying to pooh-pooh the two most popular blogging platforms out there, I've just found that for what I use these things for I can make it just fine using something simple and my own brain (which is also, perhaps, something simple, who knows). My idea of a plugin is to find the spot in the code where the new snippet will work and paste it in, which perhaps makes me a sort of Neanderthal in terms of coding, but I have yet to blow up a server or hog resources or even get my site hacked. As for antispam, I've even worked that out. One line of code. End of spam flooding.
I'm sure one day I'll eventually find something more complex (or go back to WP or something) and do things to it to make it into what I want, but until I'm big enough to take that step on my own I'll be voting "Other."