I am trying to launch the two finesse suite on different browser using Jenkins but not able to do so. Even I have parameterized my build but same browser is launching each time.
Do your execution scripts have a hard coded reference to which browser to use, or do you leave that to the system default? If system default, then it makes sense that you would have both running in the same browser since each suite is just choosing the system default (which is the same).
If you could script the registry (windows) or path (other OS) change to modify which browser is the system default, then you can override the system default browser at runtime and choose which one you want run for that thread. There may be problems if the two jobs kick off at the same time and both are trying to change the system default browser.