Unfortunately, due to the account synchronisation, whichever preference I set on one Mac automatically gets set to the same value on the other Mac. However, there's a way to solve this with the use of the Mac OS X defaults system.
What is needed is a preference setting which is specific to a certain Mac, which can be synchronised but will not apply to the other one. Technically, we need to set the preference in the preference domain for the current host, rather than for any host, which is the default (For more details, see Apple's docs). This can be done from the command line by giving the -currentHost flag to the defaults command, like so:
defaults -currentHost write com.apple.Dock orientation bottom
This will write a preference setting specific to the Mac you're working on.
[crarko adds: I haven't tested this one.]

