Draw three cards.
4, Tap: Draw a card.
Concentrate is a Sorcery, but you can’t play the Tome on your opponent’s turn either. The Tome requires only colorless mana, while Concentrate requires UU.
Are three cards in hand worth one Tome on the table?
You can play Tome purely out of Mana Drain mana. It's a quite-reasonable mana sink.
After initial casting, you *can* use the Tome on your opponent's turn.
I wouldn't assume that the game will be that short... I'd play the Book over Concentrate with no worries. Over time, I'm guessing that Book will be more useful. I'd also play Planar Portal over Book, but that's just me.
For what it's worth, I'd also play Treasure Trove over Concentrate. It costs the same as Concentrate, but if you have a lot of mana out, it can draw you more cards. Also, Library of Lat-Nam is probably more useful than Concentrate. It costs one more mana total, but one less blue total, and it's either going to do much the same thing, or it's going to be another Demonic Tutor.
Anyway, it obviously costs more for the first card with Book, Portal, or Trove, but I don't think that really matters. Over time, the slower permanents will be more useful. Plus, if you run Tolarian Academy, the extra cost over time can be fairly painless - especially with Portal, where you can fetch Academy the first time 'round if you need it.