bandages....i never ride my horse without them, if i'm being VERY lazy i bandage the back and boot the front but would never ride her without bandages on the back!!
personally for flatwork I prefer bandages to boots, unless there is a very bad brushing issue. If your horse brushes behind you can just use boots behind. I think bandages support more and you don't get as much bits of school and stuff stuck under them. For jumping though, I'd go for boots all round.
Bandages offer no more protestion I believe but Roger Smith of the RVC did a study and came to the conclusion that it does make horses more aware of "where" their legs are. Therefore may be less likely to injure themselves. Rarely known but since as I used to work with him and know he is top expert I've since used polo bandages - tend to use the one's that finish in elastic as this stops them slipping. However if I'm just hacking out around the roads I'll just pop boots on and if very wet as I'm wary of them slipping.
Brushing Boots, but decent ones. I tend to school in tendon boots nowadays as I find they have that really strong bit at the back of the tendon which is really the most important bit!