Umm, IIRC, Precog remains active till the end of the opponents turn, so you see what the opponent draws. Or am I wrong?
Yes, this is correct. Precog also reveals their entire hand as well.
So if this card only lets you see new cards that get drawn, it remains slightly less powerful than precog. Which is good since that will help keep this card from overshadowing it as much (which is what I was worried about it doing).