brace bandages are used not only for widening the gait, but support and slight protection too. Theyre good for horses that have bad suspensories, old bowed tendons, etc.
As far as them vs polos-
Support, brace bandages provide more support
Protection, polos are the way to go
If your polos are too large and bulky, you may not be putting them on tight enough. And therefore you can run into the problem of them slipping down.
I wouldnt use brace bandages on a daily basis for exercising. Really you need to be taught how to put them on since they have so much elasticity and have to be put on pretty tight in order to not slip off. Also you do not have to wear anything under them. The reason we wear cottons or rubbers under them is either a tad bit of added weight (widens the gait), or a little added protection (some horses will just slightly nick themselves without it)
As far as standing bandages, you should never use them for exercise. Those can slip way too easy and you can end up with a slew a problems such and cording, bandage bows (which is not a true bowed tendon), falls from the bandage slipping and causing misstepping..... they arent made for it