Wherever and whatever the main source of power of NCC-1701, before and after the refit, I tend to believe it would be carefully hidden out of sight, behind umpteen layers of radiation-stopping, blast-containing armor.
It would only be 24th century forcefield magic that would allow the construction of engine rooms where the annihilation focus is accessed as easily as a desk drawer, by barehanded people dressed in pajamas. Prior to that, even working close to the power transfer machinery would require protective garments (ST:TMP), and generally the engineers would prefer to stay the hell away from the active parts and only operate them by remote from centralized control rooms (TOS). Except in the early days, when Starfleet couldn't afford all that shielding and waldoing and automation, and would instead go for localized armor over key elements of the machinery (ENT).
Apart from those considerations, the powerplants of the ENT, TOS, TMP and TNG starships could be radically different in construction and mode of operation, even if all rely on matter/antimatter annihilation regulated by dilithium. There are half a dozen rather dissimilar ways to build a fission reactor today, too...