From the UK point of view, it mostly helps in deporting foreign criminals. From the House of Commons Library briefing paper on the EAW:
ACPO told us that the UK also benefits from the EAW because
it is an attractive destination for criminals. In London, 28 per cent
of people arrested are foreign nationals of which half are from the
EU. The vast majority of UK surrenders to other EU countries under the EAW are non-UK citizens — 95 per cent of over 4,000
extraditions in the four years to April 2013. In other words, most
outward EAWs concern other Member States seeking their own
citizens for crimes committed back home. This is not quite the
case for extraditions to the UK, where just over half of the 507
people surrendered were British nationals.
In relation to brexit and EU-UK cooperation on preventing crime, the BBC wrote the following:
In response, the Department for Exiting the European Union said protecting the public was an "absolute priority".
"Any drop in the breadth and quality of co-operation would have a direct impact on public safety and on our collective ability to deliver justice across Europe," a spokesman said.
Earlier this year the chief constable of the Police Service of Northern Ireland said non-participation in the scheme was "probably the biggest practical vulnerability" facing law enforcement in Northern Ireland post-Brexit.
George Hamilton told a House of Lords committee there would be "very real operational consequences if there are no alternative arrangements in place around exchange of material and people by way of a European arrest warrant".
This shows that the EAW is seen as a vital tool in policing by the UK government and high-ranking police officers (mr. Hamilton is the Chief Constable of the Police Service of Northern Ireland).