First question, because I had similar issues - do you play over a wireless connection? If that is the case, get an ethernet cable. Seriously, I was playing wireless until yesterday, and it is *much* better now with cable, although I didn't even experience stuttering a lot.
Did you have a look at the scoreboard while stuttering appears? What was your ping and pl (packet loss) at that time? If you have stuttering, I guess it's related to huge packet loss. This has nothing to do with ping itself, which explains why you have stuttering even on fast servers.
Another thing you could try is edit your network settings in Xonotic (Settings > Misc > Network), e.g. move the network speed slider to lower values and/or decrease the number of input packets.