Boots now after a recent injury after taking my horse out on a hack without any form of protection. Bandages are fine for short work but I wouldn't want to bandage up and hack for 3 - 4 hours, think they're legs would get a bit hot and sweaty.
Boots. They offer more protections to the legs and bandages dont actually support the tendons any more than boots unles you bandage all the way down the pastern- and even then the support is negligible.
I find bandages protect more of the leg than boots - they can cover a bigger area. If it's a particularly long hack or a boiling hot day I'll stick the vented boots on though, but make sure I'm not going through the woods where legs are more likely to get scratched and caught.