Hi and welcome to Orchidboard
What you're calling a Brassavola is actually a Bc Little Mermaid 'Janet', which is actually Brassocattleya (or used to be until they changed it again!
but that's another story
)
I know of folks who have Bc's mounted but I think the majority of folks would agree that potting it would be the way to go. Your vanda can do very well here in a basket with nothing, or with some bark or Epiweb to hold it in place. I also have a number of vandas just attached to a hanger with no basket at all.
Keep in mind, anything that you have mounted or hanging takes a little more time and effort to care for. Here in Florida, during the warm months...okay, most of the year
, my mounts and vandas get heavily misted at least twice a day.
If you need help with anything, let us know. The folks here are the best!
What part of Florida are you in?