For IDPA it would be SSP (Stock Service Pistol), but you could shoot it in ESP (Enhanced Service Pistol) or CDP (Custom Defensive Pistol).
At the club I shoot at, you are encouraged to shoot more than one class, they charge an extra $5 to shoot a second gun. So if you shoot in your SSP class, you could shoot again in say the ESP using the same gun. This is good especially if you travel a long ways to shoot, you get twice the shooting in.
For USPSA (IPSC), I believe you could shoot in the Prodution division. Normally you would just shoot one pistol and class as the set up is usually a lot more complex.
Go to the respective websites and the rules are posted, I think the USPSA website has an appendix that is brand specific for the class.
Also, for IDPA the holsters are a lot more restictive, and if shooting a revolver class you are limited to a 4" barrel. In IPSC just about anything goes.
Hope this helps, Ken