My horse looks like a ****** when I trailer him there is so much crap on him. Again with my "better safe than sorry" mentality I guess. Then again I have actually had a horse come flying off the highway in a trailer and walk out with little more than a few bruises because I had the forethought to put shipping boots on him.
I use shipping boots if the horse is not a kicker, and is in an angle haul or straight haul with little chance to move around. I especially use shipping boots when the stalls are partitioned to the floor to prevent the horse rubbing its legs against the partitions (I have also had this happen).
When the horse is in a box, or otherwise freestanding I wrap. If the horse can move, I don't want him to get caught up in boots. Wrapping takes longer and is way easier to screw up than just putting boots on, but it is "safer" in a box, although they won't provide as much protection. For kickers I only wrap or leave their hind legs bare. They can very easily kick boots down or off, making for a more dangerous situation.
Anyways. For shipping. I use plain plain stuff. Not a huge fan of the pillow wraps because they bunch a lot easier than the plain "no-bow" ones.
And the bandages are a lot thinner, stretchier and longer than polos (you can still get them in awesome colours though):
You should also ask whoever is wrapping your horse what they prefer to use.