I have a Jamis Coda. While some on this board say there find no difference in their speed on the Coda compared to their regular road bike, I do. Like a 3-4 mph difference in my average. I mean, my road bike weighs just under 15 lbs. and the Coda is close to 30 with my pannier on it.
Now, I use the Coda for the purpose of around town errands, going out to eat by bike, farm markets, and riding with slower friends. I've ridden it for 50 miles on the Cape Cod Rail Trail and my arms were killing me after that. Otherwise, the fit is great and it is smooth. But, I don't expect to go fast. Maybe it's because I am small?
I say go with a regular road bike with relaxed geometry or tweak your fit before you try one of the flat bar bikes.