Why do private jets such as Gulfstream fly higher than other civilian jets?
There are several reasons and none of them really have to do with a private jet being more aerodynamic than a commercial jet.

Private jets have better power to weight ratio than commercial jets so it is easier to ascend to greater heights. Commercial jets also carry more fuel which needs to be burned off to lighten the plane to go higher.

It’s easier to pressurize smaller cabins than larger ones (this is a significant factor for commercial jets).

Flying higher is usually better for avoiding weather that can even affect commercial airliners in the 30ks.

There is much less traffic up above 40k and it allows the private jets to fly more direct routes at a faster speed and more safely as well.