This is more of a legal question than a technical one, so before I answer I'll provide the usual disclaimer: IANAL.
From my (unfortunately rather extensive) experience with this, the police usually already have a good idea of who's responsible. They just have to prove it. Unfortunately, criminals these days are smart enough to wear scarves or bandanas over their face, so that only their eyes are visible to CCTV. This makes identification difficult, if not impossible. You've just got to hope that you've got a dumb one! In such a case, even a low-res blurry image of someone's face can be enough evidence to issue a warrant to search their premises, to find further evidence of graffiti or damage. It generally depends whether they can convince a judge (or the CPS, in the UK) that what they have constitutes reasonable evidence.
If you're dealing with spray-paint graffiti, they can ship paint samples off to a lab and have them matched by mass spec / IR spec. This actually resulted in a conviction in a particular case I know of, where they ended up matching the tag to a string of other graffiti incidents. The guy ended up with a hefty fine and a long suspended sentence.
However, from a technical standpoint, you're not really looking for higher resolution; you're looking for better quality pictures. Sadly, the camera industry has been pushing "MOAR MEGAPIXELZ!" as the standard for better quality, but it's simply not the case. What you're looking for is a camera with a good quality lens, decent nighttime performance, reasonable framerate, and low chromatic abberation. I'm not a photographer, so I can't really give you advice on what specs to look for, but the hard truth is that quality costs money.
My suggestion would be to go for something with a decent framerate, over something with a larger image size. See if you can arrange a demonstration with a salesperson to see what the image quality looks like, and decide for yourself whether you consider it clear enough to produce a quality picture. Also keep in mind that there's nothing to stop the vandals from attacking your camera, so don't blow a load of money on it and be surprised when it gets stolen / smashed.
Finally - get a motion-sensor light (PIR). They're cheap, easy to replace, and make vandals stick out like a sore thumb at night.