Of course it's not better than Witch in general, but it's better in some situations. It's probably better in pure BM+X. Some simulator person can probably confirm. Though I might think Witch followed by Soothsayer is best.
The big thing in Witch vs Soothsayer is that the Witch player is going to get more 5s early, both because the Witch draws, and the Soothsayer allows the Witch player to draw. So unless Gold is a lot better than the 5s early on (which shouldn't be the case with things like Minion, Labs, Upgrade, possibly Soothsayer(!)), Witch is going to have an advantage. The Soothsayer guys is just going to be picking up Golds and 3s or 4s, which is good in pure big money or possibly with Warehouse, which was the case here...
Here your opponent spent his first 2 $5 hands on Noble Brigand and Silver, which is probably not a winning strategy. If those are Apprentice and Soothsayer, he's probably ahead.