The stronger bond is formed by the better #sigma# donor, the #"NH"_3# ligand. Neither is a #pi# acceptor, which would have also strengthened the bond.
#"CO"# is a #pi# acceptor and a #sigma# donor at the same time. Is a #"M"-"CO"# bond stronger or weaker than an #"M"-"NH"_3# bond?
Between #"Cl"^(-)# and #"NH"_3#, the former is a good #pi# donor and a poor #sigma# donor, but the latter is a good #sigma# donor. Since #sigma# bonds are more direct, they contribute better to a strong bond due to more effective sharing of electron density.
In fact, a #sigma# bond is in general stronger than a comparable #pi# bond.