This is a fascinating question to consider in relation to this Dickensian classic which exposes the Victorian underworld like no other novel. I personally think that crime has changed a great deal since the days of Bill Sykes and Fagan, because crime always reflects society, and our society is incredibly different nowadays to what it was in Victorian times. This is principally because of technology and how it has impacted society.
Whilst crime such as depicted in Oliver Twist still exists in today's society, the internet and technology has created a huge new arena for crimes to be committed. Burglary now is far more common through identity theft or through hacking into banking systems and other such nefarious activities. Whilst pickpocketing still does occur, it is far more common in today's society to fall afoul of some internet scam. Another good way of thinking about this question would be to consider how would you stage or translate characters such as Bill Sykes and Fagan into modern day society. Would Sykes be some kind of internet hacker with Fagan controlling a group of computer nerds who steal people's identities rather than merely their handkerchiefs? It is an interesting question to ask.