I'd actually recommend the predecessor of Query Browser which was MySQL Control Centre. Reason being that you can create profiles which let you only list a set amount of databases, so I break projects up into connection groups. It's also slightly more usable for some things, but this might just be the familiarity issue. I've got links to both that and Mysql query browser right next to each other, and never use query browser. When i first got query browser I thought it would be great, especially after watching the site live demos, and messing about with the combined query things, but after 1/2 a day you realise it's a bit crap.
Back to the original question, of the two I'd pick phpMyAdmin.