Not necessarily, at least not to any significant degree. Depends in large part on how the bikes are set up, and again ... rider preference and objectives for the ride. If I were interested in doing organized long rides, in a group setting, and/or interested in 'personal bests' and those sorts of things -- all perfectly legitimate -- then I would probably choose drop bars. But I never have been, so I didn't and wouldn't. The latter is hypothetical; my long-distance cycling days are behind me.

That said, I still maintain there is no inherent significant difference between the two 'types' for a recreational cyclist doing a long-distance ride, especially solo : choice depends on personal preference. My preference was and is for simple flat bars w/bar ends. As it happens, the bike I used for those 'century' rides (true ones, 100+ miles) was set up (with lbs) to put me in the same position as I would have on the then-current Spec Roubaix. Position when I was 'on the grips' was slightly forward (torso angle) of where I would be on the 'tops' on a Roubaix; position on the bar ends was pretty much equivalent to where I would be on the hoods on a Roubaix. Main difference was that my arms were of course spread a bit wider (580mm as opposed to 400/420mm), so a slight 'aero' penalty there, and of course no drops. Other than that, there wasn't much in it. I miss that bike; sadly, it was stolen a couple years ago. A pic of it in 'daily driver'/ride to work mode.