Tri bikes are good if your primary interest is riding alone and even more so, alone in timed events against the clock. They're built to be ridden in the aero bar position much of the time. That position, if set up well, is fast and aerodynamic and on a full tri bike you'll have access to the shifters when down in the aero bars. You also won't have your hands near the brakes in that position which can be an issue if you ride in more urban areas where cars are more likely to surprise you from driveways and side streets. You can certainly ride them up in the base bars which is more similar to riding in the drops of a road bike. In that position you won't have ready access to the shifters but you'll have your hands near the brakes but if you end up spending most of your time up on the base bars then there's not a lot of sense in buying a dedicated tri bike.
Road bikes are more general purpose, typically climb hills much better (though that apparently isn't a concern for you) tend to be better for long days in the saddle and tend to be more comfortable with a variety of riding positions from riding up top with hands near the stem or hands on the brake hoods or hands in the drops when going faster or sprinting. All the controls are readily accessible from typical brake hoods or drops riding positions.
Basically if you don't already know that you need a tri bike for the kind of riding you intend to do then I'd strongly urge you to buy a road bike. You can always slap clip on aero bars on your road bike if you want to ride in the aerobar position but the road bike will be far more versatile for different kinds of riding and much better if you decide to join group rides as many groups discourage or flat out don't allow riders to participate while riding in the aero bars as it can lead to problems with riders in close proximity to one another riding at speed and not having their hands near their brakes.
Good luck,
-Dave
