Groups of prime order

Hi CP's! Hope someone would be so kind to help me wiht this: Is it weaker to use arithmetic mod (p-1), and hence all Zp, when suggested to work in a group of prime order q? This question is connected with discrete log signature protocols such as that in Pedersen's "Improved privacy in Wallets with Observers" or Schnorr's. I would appreciate any help ASAP, since I'm in a hurry. Please, answer me by personal mail since I'm not subscribed to the CPs list now. Thanks and best wishes from Poland. Joanna