Hmm...
I wondered the same thing, but as described by Mayall, only really bother with the Advent because the same cost in resources you deplete searching a planet can instead be spent on improving or fortifying it. It seems a little unbalanced, actually, I think the other races should simply pay less in the first place so the exploration actually gets done. But to address your question, generally only at worlds you already have a defense over (obvious reasoning: if you do find something, everyone else knows where, and will take it from you otherwise) and if a) it's early-to-mid game, 
for whatever reason you have excess resources that can't be effectively used in key research or ship production. Otherwise, I really don't bother- I get told by the game another faction has one, so I steal it.
