Well, the so called functional genes usually code for proteins instead of functional RNAs (such as tRNAs and rRNAs). Which means that they are formed by codons that will be translated into amino acids, however the genetic code is redundant, i.e. different codons can code for the same amino acid. This usually happen by the substitution of the third base of the codon. So, the variation observed in functional genes are usually greater that in rRNA genes. Therefore, it is very hard to find sections of a gene that are 100% homologous between different species for which you can design a primer that does not have any degenerate position.
I have experience with DGGE primers that are degenerate and I don't feel that they cause problems. In case you have a bad DGGE profile, just adapt your gradient to best suit your samples.