The dash as said above can operate to CATIIIa limits if a HUD is installed (50ft DH). The 737NG can be flown manually to 50ft DH if a HUD is installed or use autoland/autorollout with no DH and 75m RVR (known as CAT IIIb) depending on installed options. With minimum or no optional stuff installed the 737 can use autoland and 50ft DH (CAT IIIa).
However that is only the technical side, an operator needs to provide the relevant training and operational experience to be able to fly either plane to CAT II or CAT III limits.