I think the other important factor that the others haven't addressed is Mach number.
The speed of sound is doesn't change much with altitude (it actually drops slightly due to reducing temperature) and if a plane gets too close to it, shockwaves start to form in areas where the airflow is accelerated (such as on the top of the wing) causing a lot of excess drag.
By flying higher, a plane gets a higher ground speed and true air speed for the same indicated air speed (IAS). However the limit is when the true air speed (TAS) results in a Mach number that starts to cause shock waves. To go higher, a plane has to reduce its indicated air speed to maintain the same Mach number. Therefore the limiting height is when IAS approaches stall speed at the same time as the Mach number limit is reached. (see Coffin Corner)
Now private jets are usually designed to use smaller runways than big airliners, so they have a slower stall speed (due to relatively large wings for their weight). Their maximum Mach number is similar (an easy way to tell is that the angle of wing sweep is similar) so the height at which minimum IAS = maximum TAS is higher.
EDIT: True air speed (TAS) is the actual speed of the air, similar to the aircraft's ground speed (after allowing for wind). Indicated air speed (IAS) is the effective aerodynamic air speed, or "how much force you'd feel if you stuck your hand out the window". IAS falls relative to TAS as the air gets thinner.