Both. . . preference depending in area and purpose. Curves in the right areas, and flat in others. . .

Seriously, I have both. Preferences depend on gun type. Pistol, AR, bolt action, etc.
Pistol - I mostly have flat. Trying different ones at the moment, but I currently like the ones with a lip at the end of the trigger (for various reasons).
AR - I mostly have flat Geissle, but have curved OEM/milspec and Geissele. I haven't done shot timer tests, but I don't think I would get a measureable difference between the two.
Bolt action - I have all TT pro-curve. Mostly because what was in stock when I got my first and stuck with it. Have seen lots of various preferences. For now, I like how the pro-curve has the finger placement on a consistent level. I'll have to tune my newer TT triggers closer for more consistency. Noticeable on paper? Different guns, different loads, to can't say, but overall consistency can't hurt. I've also seen many who prefer flat triggers incorporate index points on their triggers. Though I wonder how many consistently can set/feel, say in a PRS type match where time is ticking, vice a more calm/steady shooting pace.