You will get a lot of opinions on this topic. There is no perfect geometry. Everyone is different, and the best frame for one person is not going to be the best frame for another person. I have even seen arguments against the compact frames based only on the fact that they look silly or that there is too much seat post showing. I do not care what it looks like as long as it is comfortable and efficient.
Agressive geometry is one that has the rider's back in a more horizontal, and theoretically more aerodynamic, position. A relaxed geometry is one that is more upright, which is more comfortable, but less aerodynamic.
Handling usually has more to do with top tube angle, rake, and stem length than it does with whether it is a traditional or compact geometry. The Specialized Roubaix and Trek Pilot are both compact geometry, but are among the best in terms of comfort and handling. The Giants are also compact geometry and are comfortable, but tend to be among the worst in terms of handling.
Speed has more to do with optimizing aerodynamics without causing so much discomfort that one becomes inefficient. The more aerodynamic, the faster until you get to the point that you cannot transfer power from your legs to the pedals. The point where incresed aerodynamics is offset by decreased power transfer is different for everyone.
Accelleration has a lot to do with wheel weight and power transfer. While the latter is affected by frame stiffness, it is not really a function of frame geometry. There are stiff compact frames, and there are flexy compact frames. There are flexy traditional frames, and there are stiff traditional frames. The stiff frame will accellerate faster, but it will not be as comfortable. Again, another trade-off. What good is accelleration if speed cannot be sustained. On the other hand, what good is comfort if you can never get to speed. It is all about finding the right balance, and the balance will be different depending on the ride duration and conditions.
Frame geometry is only one of many factors in determing which is the best bike for an individual rider. Even for the same rider, the best bike will be different for different rides. I would not select a bike or reject a bike solely based on wether it is a compact or traditional frame. My ride of choice, though, happens to be a Specialized Roubaix Elite.