This discussion just made me rethink what Captain Pike meant when he mentioned being tired to be responsible for "203 lives" (while I presume he includes the good doctor in his statement, it would also think he assumes responsibility for himself).
As the first ship of the new starship design, I can't imagine the other members of the UFP are just sitting still while the USS Enterprise
is put to space with an exclusive homo sapiens club, so I guess the statement suggests various alien species serving on that vessel, too, and not just "men" or human "people".
As for the crew complement (compared to Kirk's Enterprise) I always thought that Pike's Enterprise still had many bulky technology on board before Starfleet engineers like Dr. Lawrence Marvick, the designer of Kirk's
Enterprise (42 years old at the time of "Is There in Truth No Beauty?") freed up space to allow more living quarters and boost the crew complement to 430.
According to The Making of Star Trek
is already 40 years old by the time of TOS. According to Admiral Morrow the Enterprise
is 20 years old by the time of Star Trek III.
Considering the Pike Enterprise sustained heavy damage when Kirk and crew encountered the cosmic barrier in "Where No Man Has Gone Before" I never felt a quick repair job would have been sufficient to fix the damages, so I presume that Kirk got a new Enterprise Class vessel (Marvick design) which was probably intended to become USS Yorktown
(indeed Kirk's ship was originally intended to be Yorktown
before they changed the name to Enterprise).