There isn't a straight forward answer as different inserts will give you different effects in different situations. One way you should look at inserts is as if they are shock absorbers as they do as much work as your shocks do.
What i tend to do is always run the hardest insert i can (for touring cars at least). At my local track same setup, tyres, wheels, track, everything except the inserts (sorex 28 Hards compared to mediums) i am 1/4 a second quicker on a 12 second lap with the hard's. Don't sound much but its potentially worth 5 laps and probably less mistakes. Reason why is the car feels more direct, reacts quicker, generates more heat in the tyres and generally feels more stable.
But if this wasn't my local track reasons for changing to a softer insert might be;
Bumpier conditions, overheating tyres, i might need to use a harder sharper setup in bumpier conditions, or i might just need a tyre that is more forgiving between high and low bite areas. Such as paint markings, tape, dust or blue groove.
To over simplify it a lot
Hard insert = More direct, sharper, bumpier and pushes the tyre into the ground harder.
Softer insert = Less direct, smoother, more forgiving and less likely to brake away suddenly.