I love them both! If you like the Damier because of the ease of taking care of the bag, the Trevi is for pretty. It's also about $500 more than the Tivoli, so if cost is an issue that might be something to think about as you could get the Tivoli PM and a Porte Tresor International Wallet to match for the same price as the Trevi. They are both absolutely gorgeous purses. I'm waitlisted for the Tivoli PM and that's going to be my next bag, so I have a fondness for that one. But the Trevi PM is gorgeous too! You might want to call ahead though on either of these bags. I think they are both sold out and are waitlist items so he might not be able to just walk into a boutique and purchase either one on the spot.
Good luck! Let us know what you pick!