None. The limitations begin and end with the musician.
+1 Best post I have read in months.
I have both 5- and 4-stringers, and I prefer to play the 5-ers (low B) simply because so much church music is written in Bb or Eb. The fifth string makes it very, very simple to keep the same fingering patterns by making a slight shift which might not be possible on a 4-string. Still, that is not a limitation - only comfort and convenience. And, seriously, I could play every song in church that I have ever played on a 4-string...no problem.