My wife also has the Synapse and loves it. It's a very good "higher end" starter bike. But it's not an R3. I also have a Cervelo and most owners feel there is nothing better.

My advice is test rode both. If you're fairly confident you're going to stay with cycling and the R3 feels right, get it. Otherwise, go with the Synapse. But if you're like most of us, get the Synapse and continue to ride more, you'll be looking to upgrade soon. Then you waste money by buying another bike (maybe an R3) and have to sell or keep your Synapse.