A divergent exchange matrix will upweight similarities, giving longer local alignments. A stringent matrix with high identity scores will give shorter local alignments. They each offer a range of matrices from high to low sequence identity. Soft matrices are inappropropriate for searches with short motifs. A rough guide is the longer the sequence, the softer the matrix for maximal sensitivity in searches.
Softer matrices tend to give better alignments with highly divergent sequences.
Gonnet 350 can be used for high divergence.