TL;DR: Position: drop bars can be set up to match almost any reasonable flat-bar body/head position and hence visibility.
Braking: if you can squeeze your front brake from the hoods hard enough to initiate rear wheel lift-off on dry flat pavement - you're good.
The long answer: Position: Higher body/head position will generally give you better visibility. An average drop bar bike (properly fitting) will give you considerably lower body/head position than average flat bar bike (properly fitting), but this is not because of the bars per se. Rather, the manufacturers know that drop bar bikes are perceived as more "sporty" and so a bike with relatively high drops (hence less aerodynamic position) will not sell as well. Still, road bikes with high-ish drop bars are available (look for touring or "relaxed" road bikes). If you want still higher body/head position, you can use stem risers and/or adjustable stems. I can't think of any reason for reaction time to be different between drops and regular bars if body position is the same.
It's important to note, however, that higher body position means more drag and less speed; also, any position higher than touring will be less comfortable on longer/regular rides, and comfort affects safety.
Braking: Whether some particular braking setup is safe enough depends on how quickly you can stop the bike in an emergency. Because a bicycle/rider system's combined center of gravity is so high and close to the front wheel, on clean dry pavement the most braking you can get is when the rear wheel is about to lift off. Unlike with a car or even a regular motorcycle, clean dry pavement always provides enough traction to do that on a bicycle while still not skidding the front tire. BTW, that also means that rear brake is useless in an emergency on dry pavement - so don't use it!
Now, whether you can initiate rear wheel lift-off from the hoods depends on several factors - your hands' strength, your fingers' length, what type of brakes you use and, perhaps most importantly, how well tuned your whole braking system is (levers, cables, calipers, pads, rims/discs). If you can initiate that lift-off with conventional rim brakes, you can choose any bike you want (or keep existing one). If you can't, you can always upgrade something. Longer fingers are probably out of the question, and developing strength takes time, but better brakes are readily available. As of now, the most powerful solution would probably be SRAM RED 22 hydraulic hoods/levers and matching RED 22 disc brakes; much cheaper but probably just as powerful solution is TRP HY/RD hybrid (cable/hydraulic) disc brakes; there are also less integrated hybrid systems. The cheapest (and good enough for most) would be just giving your existing brakes a tune up.
Sources: Sheldon Brown, personal experience and research.