IN my opinion, the nitrile gloves give better dexterity than latex and are certainly more puncture resistant..
Some hints when trying to get gloves stocked in your squad car...
#1 - latex allergies are common... mention you may be developing one and suggest either powder free latex gloves (powder free are generally the better quality) or nitrile as an alternative
#2 - the gloves can do double duty. Depending on the administration's bent, you could call them "fingerprinting gloves", "EMS gloves", "Search gloves"...whatever, just get em in the cars.
I always try to chuck a box out of the ambulance into any open squad car trunk, if I know the unit is not equipped with them... I simply cannot understand the metality that leaves folks without proper protection...
stay safe and well