BBFC is law, PEGI used to be only guidance but as of September is now legally enforceable as well. Although there is currently a legal loophole that stops it being "official" European law, that should be closed in the forthcoming Queen's speech: http://www.joystiq.com/2009/09/08/elspa-legal-loophole-wont-delay-rollout-of-pegi-ratings/ I can imagine the BBFC ratings will be phased out sometime soon after so there's just one system.
Well, both are valid. However, the PEGI system is only a guideline whereas the BBFC classification is legally binding.
I already kinda explained it to you BBFC has now been phased out and will not be used on any new games. BBFC is now no longer legally binding and is now just a "guideline" PEGI is what every new game will have. lol~
Just to add to what the above posters have already said, yes, we're currently in a transition phase. Most games being released at the moment actually have both certificates on the box. The BBFC were not happy at all with the handover of regulation. As someone who has had to deal with entertainment regulators in the past, I have to agree with the BBFC. Aside from their misstep over the Manhunt 2 fiasco (in fairness to them, many other countries also tried to 'ban' the game), they do a very good job when classifying video games. The BBFC offer parents a massive amount of information to enable them to make informed decisions about what is or is not suitable for their child. Take the recent release of GTAIV: The Ballad of Gay Tony, here is the BBFC decision (don't forgot the click the triangle to see more), now compare that to PEGI. Four detailed long paragraphs versus three vague icons, seriously? IMO the different cultures in Europe just vary far too wildly for a single blanket ratings system to apply. I can't imagine them ever doing this for films, so why video games?
I'm with Nutech on this one, the BBFC have been really good for rating games (and films - especially as they actually post guidelines, unlike the MPAA) and post decent details about most games and films.
But the whole point is it's incredibly unlikely a parent will go and read the BBFCs findings, all they do is look on the box at the certificate. Here, BBFC lose. They just have the age rating most of the time, PEGI have the age rating and the icons giving info as to what happens in the game just as violence, bad language, drug use, spiders, etc.