We have a better and greater degree of co-operation within the EU than than we have with the US, as well as tools such as the European Arrest Warrant which are superior to extradition. Since these things are underpinned by EU agreements, it's totally unclear how much they would survive Brexit. So although it's in everyone's interest to continue co-operating and it's very likely there will be some sharing, etc. post-Brexit it's reasonable to think that it will be lesser and less effective.
Oh, and seems like a good time to point out once again that terrorism is less of a threat in the EU and the UK than it used to be:
The number of terrorist incidents has gone down, not up, and the number of people getting killed by terrorism has gone down, not up.