I prefer high boots. As above, I don't like my foulies riding up over the boot cuff. I also like that my boots have a drawstring/sealable top cuff. In both cases, the goal is to keep water out of the boots since they hold water in as well as they keep water out. I think mine are Gill brand and they do the job well enough.
Up here, I couple my boots with Merino wool socks. Because it is inevitable that your feet will be wet from sweat, rain or water but the wool will keep your feet warm where cotton will lose its heat retention properties.
Another alternative which I've seen while canoeing and on race day, is that people use Gortex socks in their regular boat shoes. This is a viable and easily packed option if you don't want to have two pairs of footwear kicking around.