  CO and CO$_2$ are the two dominant carbon-bearing molecules in comae and have
major roles in driving activity. Their relative abundances also provide strong
observational constraints to models of solar system formation and evolution but
have never been studied together in a large sample of comets. We carefully
compiled and analyzed published measurements of simultaneous CO and CO$_2$
production rates for 25 comets. Approximately half of the comae have
substantially more CO$_2$ than CO, about a third are CO-dominated and about a
tenth produce a comparable amount of both. There may be a heliocentric
dependence to this ratio with CO dominating comae beyond 3.5 au. Eight out of
nine of the Jupiter Family Comets in our study produce more CO$_2$ than CO. The
six dynamically new comets produce more CO$_2$ relative to CO than the eight
Oort Cloud comets that have made multiple passes through the inner solar
system. This may be explained by long-term cosmic ray processing of a comet
nucleus's outer layers. We find (Q$_{CO}$/Q$_{H_2O}$)$_{median}$ = 3 $\pm$ 1\%
and (Q$_{CO_2}$/Q$_{H_2O}$)$_{median}$ = 12 $\pm$ 2\%. The inorganic volatile
carbon budget was estimated to be Q$_{CO}$+Q$_{CO_2}$)/Q$_{H_2O}$ $\sim$ 18\%
for most comets. Between 0.7 to 4.6 au, CO$_2$ outgassing appears to be more
intimately tied to the water production in a way that the CO is not. The
volatile carbon/oxygen ratio for 18 comets is C/O$_{median}$ $\sim$ 13\%, which
is consistent with a comet formation environment that is well within the CO
snow line.
