Jessica, no difference in the firearms themselves. The LE version is specifically marked by the manufacturer for sale to LE/QP.First Responders. The LE version normally has a QP discount whereas the standard 590A1 does not. No firearm difference.

Jessica, Exactly same firearm.

exact same gun the LE is a LE discount program "Many major manufacturers offer discounts to a large list of individuals they consider Qualified Professionals. Although commonly referred to as Law Enforcement, LE or Veterans Discounts, these discounts are actually also available to many other types of Qualified Professionals, including Active, Honorably Discharged or Retired Military personnel - all branches (veterans, including medical discharges/disabled) National Guard personnel - all branches Military Reserve personnel - all branchesCAP - Civil Air Patrol
Fire Fighters - including volunteers
Paramedics and EMTs
TSA Employees
Commercial Pilots
Federal Flight Deck Officers
Air Marshals
Court Judges
District and Deputy District Attorneys
All sworn or retired Law Enforcement Officers - city, county, state, and federal
All Corrections and Probation Officers
State Licensed Security Companies
State, Federal, and Private Security Guards
DOD Contractors and the link
budsgunshop.com/catalog/qualified_professional_discounts.php"

Really, there isn't any difference. LE basically means law enforcement, which if you are a qualified person you get a discount on the firearm, normally.