Don't base major buying decisions on misconceptions. Tri bikes aren't faster, it's the set up of the rider on it that is intended for faster riding... but it's only for relatively short races, and definitely not for great handling or much climbing. Tri bikes position the rider more forward and down. The only advantage is a more aero position, but it's not the kind of position that a normal person would want to ride in on a regular basis for long rides. If you really want to experience the thrill of a fine handling bike that will allow you to make the best of your abilities in a variety of conditions, get the road bike. There's nothing stopping you from positioning yourself more as on a tri bike on the road bicycle if that's what you want, but at least with the road bike, you get the versatility.
Road riding is not about sheer speed at all times. Any bike which positions the rider forward is a bike that must be ridden all out at all times, or else it quickly becomes very uncomfortable due to having all your weight forward.
As an analogy, think of the hot rod with super wide tires at the back versus the sports car. Which would you rather be driving around twisty, hilly country roads?
On the other hand, if you get the tri bike, that should generate a lot of interesting future questions about saddle pain, back pain, hand numbness, etc.