Keep in mind if you paint it black it is virtually impossible to restore it to what it was if you need to. eg., if you had a massive scratch on the front panel and the tank was small enough that you could drain it and flip it around to the pristine back panel.
Why don't you do a trial and buy a roll of black plastic background or whatever colour you want from your LFS and stick it to the outside of the back glass and see if you like it before you take the plunge? If your fish are lighter coloured it will make them pop, but may make darker coloured ones camouflaged. eg., my mate had black tahitian moon sand, black background, and had a foot long black shark in his tank that I could never really see.