There is probably less serious crime (for the population size) than in the "good old days", but it gets reported far far more often.
For example a missing child these days is usually a fairly big thing, often national news until the child is found.
But back in the old days it would likely only have been local news.
So the perception is that children are going missing more (especially that they're being kidnapped/abused and killed by strangers).
The same with say murders, in the old days it was only really horrific or unusual murders that might have made the national papers for a day or two, now virtually any murder has a good chance of becoming national news via the TV, Radio, Internet (within minutes/hours) and papers.
So the perception is it happens more.
And the same with again with child abuse, it used to be very very poorly recorded, often not even reported or people told the child to stop being stupid and lying.
Now it is quite likely to be reported, almost certain to be recorded and investigated.
So the perception is that back in the good old days children were not abused, when in reality they were far more likely to have been abused but it was never investigated or (as seems to have been the case far too often with various religious groups), when it was reported the children were told to shut up, and the criminal quietly moved to another area (IIRC the Catholic church in America has paid out hundreds of millions, if not billions of pounds in compensantion over such cover ups).
Of course there are some crimes that are more common now, or simply recognised as a crime now so the stats for them are up (in some cases simply because as I say it is now known as a crime).
Motoring offences are almost certainly up on what they were in the 40's and 50's, even if you discount Speeding (which went up massively simply because technology meant it was possible to catch more people and deal with them), but also simply because more people are now driving, and they're driving more.