Nah, David Brent is just a well meaning incompetent fool where as Rimmer :
"Rimmer's primary character traits include anal-retentiveness, over-adherence to protocol, cowardice, bitterness and a severely inflated ego which is likely a coping mechanism for his deep-seated sense of self-loathing, which he tries but sometimes fails to hide from others. As the highest ranking survivor aboard the ship (despite being a hologram), Rimmer often deludes himself into believing that he is in charge and that he has somehow been moulding "his" crew into an effective spacegoing unit"
NB Shamelessly lifted from Wikipedia as I couldn't be arsed typing.