NF3 is stable as the sizes of fluorine and nitrogen are comparable and the bonding interaction is good enough to give a stable compound.
However, the sizes of chlorine and nitrogen are quite different. The bonding interaction between 2p of nitrogen and 3p of chlorine is not sufficiently strong leading to an unstable nitrogen trichloride.
Also since chlorine atoms are larger than fluorine, the lone pair-lone pair and lone-pair bond-pair repulsion is also larger rendering nitrogen trichloride even more unstable.