aio_suspend (3) - wait for asynchronous I/O operation or timeout
pasuspender (1) - Temporarily suspend PulseAudio
pm-action (8) - Suspend or Hibernate your computer
pm-hibernate (8) - Suspend or Hibernate your computer
pm-is-supported (1) - Test whether suspend or hibernate is supported.
pm-suspend (8) - Suspend or Hibernate your computer
pm-suspend-hybrid (8) - Suspend or Hibernate your computer
rt_sigsuspend (2) - wait for a signal
sigsuspend (2) - wait for a signal
usleep (3) - suspend execution for microsecond intervals
usleep() is a function. It could be what my system uses.
Words like sleep and suspend are definitely overloaded. Ignore functions like sleep/usleep/nanosleep, which just cause the current process to not do anything for the specified time. Also ignore anything related to signal handlers or SIGSTOP (a signal used to suspend processes). pm-suspend looks like a candidate, but the best way to figure out if xubuntu calls it is to look at the source code.
Keep in mind that it's even possible that ubuntu and xubuntu use the same command/function to suspend but that it works better in xubuntu for some other reason, like maybe a lack of compiz.