The main differences between the Hyperion and the Odysseus classes were that the Hyperion had a larger internal volume, even though it wasn't too much bigger, and it had a bit more advanced warp drive, allowing it to go faster and explore farther reaches of space. The weapons and shield systems of the Hyperion were slightly improved by channeling the laser and particle beam power conuits through the main impulse fusion reactors. Starfleet R&D had also managed to change the laser emission hard points so that they could be switched from firing lasers to particle beams instantaneously. Thus, extra weapons ports were not needed for the particle acceleration cannons. It is this improvement which eventually allowed Starfleet scientists to make a leap forward into a combination of energy and particle weapons which came to be known as the phasers in use today.
Even once the Constitution class was built, the Hyperion remained a mainstay in the exploration of Federation space for quite some time. They took advantage of the later inventions of such technology as transporters, phasers, and photon torpedoes.
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