Each of these has their own merits, and it's too bad we can't mix the two approaches, somehow!  The first way gives more potential for spookiness and for the characters to use their psychic talents, but I'm also for story enrichment and getting all the information we can.  I suppose if I had to pick one choice over the other, I'd go with B), and it'll really be interesting if the other player decides to go with A)!  Lol.  Then we'll be stuck, unless you just pick one, since you're the GM of things.