The GnuTLS @certtool@ only generates "DSA" parameters (any prime with a large generator), while @openssl@ can generate "DH" parameters with a generator of 2 or 5 combined with a Sophie Germain prime @(p-1)/2@ (i.e. both @p@ and @(p-1)/2@ are primes) or "DSA" parameters using the @-dsaparam@ option.
"DH" parameters take a lot more time to generate, but you can reuse keys for those. Keys for "DSA" parameters should not be reused, i.e. one should generate a new private key for each connection, which is the case in mod_gnutls. The default parameters provided by lighttpd are "DH" parameters.
"DH" parameters take a lot more time to generate, but you can reuse keys for those (although it is not recommended, search for @SSL_OP_SINGLE_DH_USE@ in the openssl manual on @SSL_CTX_set_tmp_dh_callback@). Keys for "DSA" parameters should not be reused, i.e. one should generate a new private key for each connection, which is the case in mod_gnutls. The default parameters provided by lighttpd are "DH" parameters.