I know most people boom from the top down but occasionally I've seen people boom from the bottom.

Lets say two characters are standing up and having a convo on OTS form and the only way I can boom it is to mount my mic on on a tiny photography tripod on let's say a table beneth them. The other option is to use a light sttand with an arm and have the mic above them. It there an advantage in the sound from mounting it above them on a light stand then having it below them on table even if it's its the same distance from their mouths both ways?

I have boomed both ways. With mic proximity to subject the same, there was no sound diff that I could discern. I boomed from the bottom because of framing issues - Generally I boom from above. Cannot always do that though.

The advantage of booming from top is that you avoid reflections from the floor.

really, what floor you are talking about , the real one or one that on the ceiling :-)

the only benefit from the top ( if the frame aloud the both positions in the same distance )that the actors can work or talk with their hands .
and usially if they moove you almost cant do it .
outside where you have allot of urban noise the under booming will be better not to get the ground reflection

These scenarios are why God invented wireless mics.