It should be noted that a variation of the SIG 225 is the SIG P6, a West German police handgun from the 70's and 80's. In some films, it may actually be the SIG P6, rather than the P225, but for the sake of argument, the two are interchangeable.
Notable differences between the SIG 225 and the SIG P6 are that the P6 has a much heavier mainspring (giving it an intensely heavy DA pull) and a cruder feed ramp, thus lowering reliability with hollow point rounds. The P225, being a commercial weapon, was available with tritium night sights, while the P6 has standard iron sights.
Bourne has used the P225 in the Identity, Supremacy, Ultimatum, and Jason Bourne films.